{
  "schema_version": 1,
  "retrieved": "2026-11-03",
  "scope": "Complete six-section Forum link inventory and pinned Optlib module/README mathematical-resource inventory. Not a theorem audit or full-paper import.",
  "forum": {
    "url": "https://optimization-x-ai.github.io/resources/",
    "sha256": "6ef965b0919decaf9f25be75dff1a5d2515c554d52b0836df592c40084e7e84b",
    "bytes": 47494,
    "upstream_updated": "2026-10-30",
    "license": "not-established",
    "reuse": "Bibliographic titles, links and listed dates only; no copied prose, layout, code or proofs.",
    "verification": "Page inventory only; papers and their claimed AI involvement are not independently audited.",
    "sections": [
      {
        "id": "ai_assisted_workflow",
        "title": "AI-Driven Optimization Research",
        "items": [
          {
            "title": "Peppy: An AI-Assisted Workflow for Tight Convergence Analysis of Optimization Algorithms",
            "url": "https://arxiv.org/abs/2609.35762",
            "listed_date": "2026-09-28",
            "status": "external-reference",
            "id": "forum-bf11ea0bbc5a8cae"
          },
          {
            "title": "Auditing Optimization Papers with Agentic AI",
            "url": "https://web.stanford.edu/~udell/doc/udell26_ai_review_sos.html#/title-slide",
            "listed_date": "2026-08-24",
            "status": "external-reference",
            "id": "forum-40b11990a92b653a"
          },
          {
            "title": "A Domain-Specific Harness for End-to-End Automation of Optimization Research",
            "url": "https://arxiv.org/abs/2608.07407",
            "listed_date": "2026-08-07",
            "status": "external-reference",
            "id": "forum-218483d838fc395e"
          },
          {
            "title": "Advancing Mathematics Research with AI-Driven Formal Proof Search",
            "url": "https://arxiv.org/abs/2605.22763",
            "listed_date": "2026-05-21",
            "status": "external-reference",
            "id": "forum-1d4ccde51829bfc0"
          },
          {
            "title": "ImprovEvolve: Basin-Hopping Meets LLM-Guided Evolutionary Search",
            "url": "https://arxiv.org/abs/2602.10233",
            "listed_date": "2026-02-10",
            "status": "external-reference",
            "id": "forum-8754425991f401ec"
          },
          {
            "title": "AI and the future of optimization modeling",
            "url": "https://web.stanford.edu/~udell/doc/udell24_optimus_informs_slides.pdf",
            "listed_date": "2024-10-21",
            "status": "external-reference",
            "id": "forum-49b2030c4ad4661c"
          },
          {
            "title": "OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale",
            "url": "https://arxiv.org/abs/2407.19633",
            "listed_date": "2024-06-29",
            "status": "external-reference",
            "id": "forum-6810f61abc83e4c3"
          },
          {
            "title": "OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models",
            "url": "https://arxiv.org/abs/2402.10172",
            "listed_date": "2024-02-15",
            "status": "external-reference",
            "id": "forum-26173ee5c7f1fdab"
          },
          {
            "title": "Guiding RL Agents with Classical Algorithms and Heuristics to Solve Combinatorial Optimization Problems on Graphs",
            "url": "https://openreview.net/forum?id=KkBU26V20i",
            "listed_date": "2023-09-23",
            "status": "external-reference",
            "id": "forum-13f8172092c811e3"
          }
        ]
      },
      {
        "id": "formal_methods",
        "title": "Formal Verification",
        "items": [
          {
            "title": "Optlib",
            "url": "https://github.com/optsuite/optlib",
            "listed_date": null,
            "status": "external-reference",
            "id": "forum-99b5a0da56076b9c"
          }
        ]
      },
      {
        "id": "education",
        "title": "Optimization Education",
        "items": [
          {
            "title": "Open Problems as Active Learning in the Age of AI",
            "url": "https://odi.inf.ethz.ch/blog/teaching-with-open-problems/",
            "listed_date": "2026-09-15",
            "status": "external-reference",
            "id": "forum-c7b66f4c60e1ee74"
          }
        ]
      },
      {
        "id": "modeling",
        "title": "AI-Assisted Works on Optimization Modeling",
        "items": [
          {
            "title": "Computing Multi-Slot First-Price Pacing Equilibria at Scale via Entropic Smoothing",
            "url": "https://arxiv.org/abs/2610.24323",
            "listed_date": "2026-10-16",
            "status": "external-reference",
            "id": "forum-546d4bc1e530477d"
          },
          {
            "title": "Are Single-Leader-Multi-Follower Problems Particular Cases of Bilevel Optimization?",
            "url": "https://arxiv.org/abs/2610.23458",
            "listed_date": "2026-10-16",
            "status": "external-reference",
            "id": "forum-e1a191047e08b7a2"
          },
          {
            "title": "Utility-Based Recovery Risk Measures: Redundancy and Approximation for Portfolio Optimization",
            "url": "https://arxiv.org/abs/2610.13454",
            "listed_date": "2026-10-09",
            "status": "external-reference",
            "id": "forum-61c9917e22fd3d3c"
          },
          {
            "title": "The Geometry of Anisotropic Dilation for Optimal Regularization",
            "url": "https://arxiv.org/abs/2610.09310",
            "listed_date": "2026-10-07",
            "status": "external-reference",
            "id": "forum-d29357fbcc3550d2"
          },
          {
            "title": "Sliced Wasserstein Barycenters: The Analysis Approach within the Barycentric Coding Model in the Wasserstein Space",
            "url": "https://arxiv.org/abs/2610.08734",
            "listed_date": "2026-10-06",
            "status": "external-reference",
            "id": "forum-e7f3a6325404494d"
          },
          {
            "title": "More on Disjunctive Convex Hulls of Generalized Cross Polytopes",
            "url": "https://arxiv.org/abs/2610.05560",
            "listed_date": "2026-10-04",
            "status": "external-reference",
            "id": "forum-49b6bfad0a01ac6d"
          },
          {
            "title": "Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope",
            "url": "https://arxiv.org/abs/2609.25981",
            "listed_date": "2026-09-22",
            "status": "external-reference",
            "id": "forum-d6d28a072312a6f0"
          },
          {
            "title": "Quadratic Convexification of a Square Truncated by a Hyperbola",
            "url": "https://arxiv.org/abs/2608.26639",
            "listed_date": "2026-08-27",
            "status": "external-reference",
            "id": "forum-8fb6ed98d96f7b69"
          },
          {
            "title": "Joint-Range Inequalities for Nonconvex QCQPs",
            "url": "https://arxiv.org/abs/2608.03318",
            "listed_date": "2026-08-04",
            "status": "external-reference",
            "id": "forum-8a260bc595a44f5c"
          },
          {
            "title": "Composition and tensor train structure in polynomial optimization",
            "url": "https://arxiv.org/abs/2604.17563",
            "listed_date": "2026-04-19",
            "status": "external-reference",
            "id": "forum-7a0c3ea5168259f9"
          },
          {
            "title": "Semidefinite relaxations for nonlinear elasticity with energies convex in the Cauchy-Green strain tensor",
            "url": "https://arxiv.org/abs/2604.13566",
            "listed_date": "2026-04-15",
            "status": "external-reference",
            "id": "forum-73f7c845aa65e6d4"
          },
          {
            "title": "Polyconvexity with Moments and Sums of Squares",
            "url": "https://arxiv.org/abs/2604.11124",
            "listed_date": "2026-04-13",
            "status": "external-reference",
            "id": "forum-aa155d170c73d76f"
          }
        ]
      },
      {
        "id": "algorithms",
        "title": "AI-Assisted Works on Algorithm Design and Analysis",
        "items": [
          {
            "title": "DREAM: Delay-Resistant Acceleration with Momentum",
            "url": "https://arxiv.org/abs/2610.37444",
            "listed_date": "2026-10-27",
            "status": "external-reference",
            "id": "forum-4ae3e0318f0c2e30"
          },
          {
            "title": "Continuous-time analysis and algorithms for linear and convex quadratic programs via exactly solvable differential inclusions",
            "url": "https://arxiv.org/abs/2610.30300",
            "listed_date": "2026-10-21",
            "status": "external-reference",
            "id": "forum-c11d4e5788d5c0d3"
          },
          {
            "title": "A short proof of a range-relative FPTAS for polynomial integer optimization over bounded polyhedra",
            "url": "https://arxiv.org/abs/2610.29573",
            "listed_date": "2026-10-21",
            "status": "external-reference",
            "id": "forum-ee70360a93e6da0e"
          },
          {
            "title": "Weak-$L^α$ Noise, Strong Guarantees: Gradient Clipping under Affine Heavy Tails",
            "url": "https://arxiv.org/abs/2610.28107",
            "listed_date": "2026-10-20",
            "status": "external-reference",
            "id": "forum-58054e24050ed98e"
          },
          {
            "title": "Gradient descent reaches arbitrary accuracy in a fixed number of large steps on multiclass logistic regression",
            "url": "https://arxiv.org/abs/2610.26748",
            "listed_date": "2026-10-19",
            "status": "external-reference",
            "id": "forum-eb27f2145d16ada1"
          },
          {
            "title": "On the Nonoccurrence of Gradient Restart in Nesterov Accelerated Gradient Method",
            "url": "https://arxiv.org/abs/2610.26546",
            "listed_date": "2026-10-19",
            "status": "external-reference",
            "id": "forum-ec188e8e15dcdbff"
          },
          {
            "title": "Acceleration of Generalized Conditional Gradient Methods",
            "url": "https://arxiv.org/abs/2610.25473",
            "listed_date": "2026-10-18",
            "status": "external-reference",
            "id": "forum-efd597c618858c24"
          },
          {
            "title": "Accelerating Finite-Sum Bilevel Optimization with Fully First-Order Oracles",
            "url": "https://arxiv.org/abs/2610.24538",
            "listed_date": "2026-10-17",
            "status": "external-reference",
            "id": "forum-4ff003117da6b579"
          },
          {
            "title": "Optimal degree bounds for sum-of-squares representations",
            "url": "https://arxiv.org/abs/2610.24638",
            "listed_date": "2026-10-17",
            "status": "external-reference",
            "id": "forum-c2030167b7be22f6"
          },
          {
            "title": "Convergence Rates for Lasserre's Upper-Bound Hierarchy on $\\mathbb{R}^d$ with Gaussian Measure",
            "url": "https://arxiv.org/abs/2610.22030",
            "listed_date": "2026-10-15",
            "status": "external-reference",
            "id": "forum-c77178b430320581"
          },
          {
            "title": "Envelope Cubic Regularized Newton Method for Nonconvex-Strongly-Concave Minimax Optimization",
            "url": "https://arxiv.org/abs/2610.20345",
            "listed_date": "2026-10-14",
            "status": "external-reference",
            "id": "forum-90b480f9af3ed7d4"
          },
          {
            "title": "First-order Optimization Methods with Generalized Smoothness for Low-rank Matrix Factorization",
            "url": "https://arxiv.org/abs/2610.19059",
            "listed_date": "2026-10-13",
            "status": "external-reference",
            "id": "forum-b41813fb536787b9"
          },
          {
            "title": "Cyclic steepest descent is $R$-superlinearly convergent for almost every initialization on two-spectrum quadratics",
            "url": "https://arxiv.org/abs/2610.15335",
            "listed_date": "2026-10-11",
            "status": "external-reference",
            "id": "forum-052761c19eeab4e9"
          },
          {
            "title": "Adaptive two-points zero-order accelerated methods for stochastic convex optimization problems",
            "url": "https://arxiv.org/abs/2610.15202",
            "listed_date": "2026-10-10",
            "status": "external-reference",
            "id": "forum-823a57f2977941a5"
          },
          {
            "title": "The exact worst-case asymptotic rate of Nesterov acceleration for strongly convex optimization",
            "url": "https://arxiv.org/abs/2610.15125",
            "listed_date": "2026-10-10",
            "status": "external-reference",
            "id": "forum-2ff099e4ee991122"
          },
          {
            "title": "Optimal Algorithms for Nonsmooth Nonconvex Stochastic Optimization with Constraints",
            "url": "https://arxiv.org/abs/2610.13787",
            "listed_date": "2026-10-09",
            "status": "external-reference",
            "id": "forum-78caf88d1e62dbb5"
          },
          {
            "title": "Matching the Lower Bounds: Stochastic Contracting Cubic Newton and Its Optimal Acceleration",
            "url": "https://arxiv.org/abs/2610.11693",
            "listed_date": "2026-10-08",
            "status": "external-reference",
            "id": "forum-c4f97e5ae65c58ec"
          },
          {
            "title": "Accelerated Proximal Gradient Method for Non-Strongly Convex Time-Varying Optimization",
            "url": "https://arxiv.org/abs/2610.11425",
            "listed_date": "2026-10-08",
            "status": "external-reference",
            "id": "forum-5aabe1595e453632"
          },
          {
            "title": "SDDP has polynomial iteration complexity in the horizon",
            "url": "https://arxiv.org/abs/2610.12713",
            "listed_date": "2026-10-08",
            "status": "external-reference",
            "id": "forum-0cc589e52bbf2208"
          },
          {
            "title": "Polynomial Acceleration of Alternating Projections: Chebyshev Acceleration, Convergence Rates, and Retractions",
            "url": "https://arxiv.org/abs/2610.06150",
            "listed_date": "2026-10-05",
            "status": "external-reference",
            "id": "forum-641546748a6f121f"
          },
          {
            "title": "Optimal Oracle Complexity for Finite-Sum Monotone Inclusions",
            "url": "https://arxiv.org/abs/2610.05038",
            "listed_date": "2026-10-04",
            "status": "external-reference",
            "id": "forum-ee65612bbd158860"
          },
          {
            "title": "Finding Stationary Points under Higher-Order Smoothness: Trapping Algorithms and First-Order Lower Bounds",
            "url": "https://arxiv.org/abs/2610.02791",
            "listed_date": "2026-10-02",
            "status": "external-reference",
            "id": "forum-4a2c0d0d07f510d9"
          },
          {
            "title": "Boundary Geometry and Global Rates of Cyclic Coordinate Descent for SVM Duals",
            "url": "https://arxiv.org/abs/2609.39240",
            "listed_date": "2026-09-30",
            "status": "external-reference",
            "id": "forum-675303c8d439cc3b"
          },
          {
            "title": "Acceleration for Affine-coupling problems",
            "url": "https://arxiv.org/abs/2609.36997",
            "listed_date": "2026-09-29",
            "status": "external-reference",
            "id": "forum-1dc4f87292fe2d66"
          },
          {
            "title": "Greedy sign-based box splitting: exact solvable classes, sharp thresholds and order-oracle complexity",
            "url": "https://arxiv.org/abs/2609.37444",
            "listed_date": "2026-09-29",
            "status": "external-reference",
            "id": "forum-040daf67a0db2ac6"
          },
          {
            "title": "Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding",
            "url": "https://arxiv.org/abs/2609.36033",
            "listed_date": "2026-09-28",
            "status": "external-reference",
            "id": "forum-cd9e356bd776d774"
          },
          {
            "title": "Accelerated Algorithms for Stochastic Monotone Inclusions with Fixed Queries",
            "url": "https://arxiv.org/abs/2609.35631",
            "listed_date": "2026-09-28",
            "status": "external-reference",
            "id": "forum-b86e10850543cab1"
          },
          {
            "title": "Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memory",
            "url": "https://arxiv.org/abs/2609.33814",
            "listed_date": "2026-09-27",
            "status": "external-reference",
            "id": "forum-1f2ea4dc3ebd53c5"
          },
          {
            "title": "AltGDA Achieves Global $O(1/T)$ Ergodic Convergence in Matrix Games",
            "url": "https://arxiv.org/abs/2609.32995",
            "listed_date": "2026-09-26",
            "status": "external-reference",
            "id": "forum-c8406a3de4760fbf"
          },
          {
            "title": "Anchored Extra-Proximal Methods: Optimal Higher-Order Methods for Monotone Inclusion Problems",
            "url": "https://arxiv.org/abs/2609.30212",
            "listed_date": "2026-09-24",
            "status": "external-reference",
            "id": "forum-653b9210ae0e72b4"
          },
          {
            "title": "Optimal High-Order Methods for Solving Monotone Variational Inequalities",
            "url": "https://arxiv.org/abs/2609.23557",
            "listed_date": "2026-09-20",
            "status": "external-reference",
            "id": "forum-08a5665eb05db1fe"
          },
          {
            "title": "Moving-Average Iteration of Linear Maps",
            "url": "https://arxiv.org/abs/2609.21442",
            "listed_date": "2026-09-18",
            "status": "external-reference",
            "id": "forum-426b72c725bf7e18"
          },
          {
            "title": "Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates",
            "url": "https://arxiv.org/abs/2609.20701",
            "listed_date": "2026-09-17",
            "status": "external-reference",
            "id": "forum-9270672bf016242a"
          },
          {
            "title": "The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings",
            "url": "https://arxiv.org/abs/2609.20687",
            "listed_date": "2026-09-17",
            "status": "external-reference",
            "id": "forum-f8f9de1b2ff361c3"
          },
          {
            "title": "Bounded Integer Quadratic Programming through Parallelepiped Covers and Discrete Convic Optimization",
            "url": "https://arxiv.org/abs/2609.17889",
            "listed_date": "2026-09-15",
            "status": "external-reference",
            "id": "forum-6a13dc9f68508ff6"
          },
          {
            "title": "Optimal Recursive Composition and Dyadic Phase Laws for Gradient Descent with Predetermined Stepsizes",
            "url": "https://arxiv.org/abs/2609.11788",
            "listed_date": "2026-09-10",
            "status": "external-reference",
            "id": "forum-6a11428bd12306d8"
          },
          {
            "title": "Constant Steps Are s-Composable: An Exact Interpolation Certificate for Gradient Descent",
            "url": "https://arxiv.org/abs/2609.11784",
            "listed_date": "2026-09-10",
            "status": "external-reference",
            "id": "forum-86ec94268b8d21eb"
          },
          {
            "title": "Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth",
            "url": "https://arxiv.org/abs/2609.11480",
            "listed_date": "2026-09-10",
            "status": "external-reference",
            "id": "forum-3f23433793b20185"
          },
          {
            "title": "An $O(1/T^3)$ algorithm for minimizing convex quadratic functions over the $L_1$ ball",
            "url": "https://arxiv.org/abs/2609.10314",
            "listed_date": "2026-09-09",
            "status": "external-reference",
            "id": "forum-fe45096d6e0c161d"
          },
          {
            "title": "Heavy-Ball Method under Randomized Schedules",
            "url": "https://arxiv.org/abs/2609.09743",
            "listed_date": "2026-09-09",
            "status": "external-reference",
            "id": "forum-9d332272cf5a09f5"
          },
          {
            "title": "The Exact Time-Uniform Rate Frontier for Stochastic Gradient Descent on Smooth Convex Objectives",
            "url": "https://arxiv.org/abs/2609.08537",
            "listed_date": "2026-09-08",
            "status": "external-reference",
            "id": "forum-0da058cdc1fd972d"
          },
          {
            "title": "On Minimax Optimality and Uniqueness of Fixed-Step First-Order Methods for Smooth Convex Optimization",
            "url": "https://arxiv.org/abs/2609.07671",
            "listed_date": "2026-09-07",
            "status": "external-reference",
            "id": "forum-bdedb477379db2d2"
          },
          {
            "title": "Centered Permutation Prefixes for SGD with Random Reshuffling: Sharp Rates, Hölder Geometry, and Composite Proximal Extensions",
            "url": "https://arxiv.org/abs/2609.04578",
            "listed_date": "2026-09-04",
            "status": "external-reference",
            "id": "forum-e5a201667c9b2753"
          },
          {
            "title": "Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman--Pereira Matrices",
            "url": "https://arxiv.org/abs/2609.01010",
            "listed_date": "2026-09-01",
            "status": "external-reference",
            "id": "forum-25b1f2cf4e1de726"
          },
          {
            "title": "Optimal Parameter-Free Gradient Minimization in $\\ell_p$ Geometry",
            "url": "https://arxiv.org/abs/2608.26688",
            "listed_date": "2026-08-27",
            "status": "external-reference",
            "id": "forum-c5cef834916c9339"
          },
          {
            "title": "When a Relaxed PEP Is Exact: The Sharp Queried-Gradient Rate of Nesterov's Fast Gradient Method",
            "url": "https://arxiv.org/abs/2608.26719",
            "listed_date": "2026-08-27",
            "status": "external-reference",
            "id": "forum-a09def27c4530fc1"
          },
          {
            "title": "Zeroth-Order Nonsmooth Nonconvex Optimization with Convex Liftings and Its Application to State-Feedback $H_\\infty$ Policy Optimization",
            "url": "https://arxiv.org/abs/2608.23178",
            "listed_date": "2026-08-24",
            "status": "external-reference",
            "id": "forum-a5caa2871a174b6a"
          },
          {
            "title": "Doubling the dimension yields a benign landscape for the squared-stress",
            "url": "https://arxiv.org/abs/2608.16799",
            "listed_date": "2026-08-17",
            "status": "external-reference",
            "id": "forum-ccc37e697093112f"
          },
          {
            "title": "On the Complexity of BFGS Method for Smooth Convex Optimization",
            "url": "https://arxiv.org/abs/2608.16009",
            "listed_date": "2026-08-17",
            "status": "external-reference",
            "id": "forum-d61aab3251ce14c1"
          },
          {
            "title": "Radial-type error bounds for semidefinite feasibility problems without strict feasibility: qualitative estimates and asymptotic tightness",
            "url": "https://arxiv.org/abs/2608.09013",
            "listed_date": "2026-08-10",
            "status": "external-reference",
            "id": "forum-eb28fe8fe78522ba"
          },
          {
            "title": "Halpern Iteration Achieves $\\tilde{\\mathcal{O}}(ε^{-1/p})$ $p$th-Order Oracle Complexity for Monotone Variational Inequalities",
            "url": "https://arxiv.org/abs/2608.08463",
            "listed_date": "2026-08-09",
            "status": "external-reference",
            "id": "forum-58c9e96a416614dc"
          },
          {
            "title": "Forward-Reflected-Backward algorithm with Linesearch",
            "url": "https://arxiv.org/abs/2607.20113",
            "listed_date": "2026-07-22",
            "status": "external-reference",
            "id": "forum-afd7fb6664841703"
          },
          {
            "title": "Improved Convergence Rate for Stochastic Multi-Gradient Descent: A Proof Discovered with AI",
            "url": "https://arxiv.org/abs/2607.18174",
            "listed_date": "2026-07-20",
            "status": "external-reference",
            "id": "forum-599d5eec3d04c95d"
          },
          {
            "title": "From Manifold Identification to Newton Acceleration on Intersections: Sparse Stiefel Optimization",
            "url": "https://arxiv.org/abs/2607.12877",
            "listed_date": "2026-07-14",
            "status": "external-reference",
            "id": "forum-4fc9cea09f1b733a"
          },
          {
            "title": "Sharp $O(1/k)$ convergence rate for the Sinkhorn algorithm via a local analysis",
            "url": "https://arxiv.org/abs/2606.28973",
            "listed_date": "2026-06-27",
            "status": "external-reference",
            "id": "forum-eb77db4684485a86"
          },
          {
            "title": "Accelerated and Stable Convergence with Anchored Generalized Optimistic Method",
            "url": "https://arxiv.org/abs/2606.21528",
            "listed_date": "2026-06-19",
            "status": "external-reference",
            "id": "forum-b348424a72ee6ea9"
          },
          {
            "title": "Unified Ergodic Primal-Dual Gap Rates with Unhalved Primal Stepsizes",
            "url": "https://arxiv.org/abs/2606.21482",
            "listed_date": "2026-06-19",
            "status": "external-reference",
            "id": "forum-3ddc02f5dfd8ec77"
          },
          {
            "title": "Last-Iterate Convergence of Optimistic Multiplicative Weight Update",
            "url": "https://arxiv.org/abs/2606.11773",
            "listed_date": "2026-06-10",
            "status": "external-reference",
            "id": "forum-00c2ec71f56b1c27"
          },
          {
            "title": "Accelerating Min-Max Optimization via Power-Law Stepsizes",
            "url": "https://arxiv.org/abs/2606.01764",
            "listed_date": "2026-06-01",
            "status": "external-reference",
            "id": "forum-043826b2ccf293ac"
          },
          {
            "title": "Efficient Gradient Methods for Distributed Saddle Problems",
            "url": "https://arxiv.org/abs/2605.18604",
            "listed_date": "2026-05-18",
            "status": "external-reference",
            "id": "forum-48724f298736d766"
          },
          {
            "title": "Almost-sharp $O(k^{-1} \\log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case",
            "url": "https://arxiv.org/abs/2604.26265",
            "listed_date": "2026-04-29",
            "status": "external-reference",
            "id": "forum-abee19452fd90483"
          },
          {
            "title": "Boţ-Nguyen Acceleration, Weighted Mean Ergodic Iteration, and the Beta-Binomial Distribution",
            "url": "https://arxiv.org/abs/2604.17084",
            "listed_date": "2026-04-18",
            "status": "external-reference",
            "id": "forum-e833f1ff713f0ad1"
          },
          {
            "title": "An Improved Last-Iterate Convergence Rate for Anchored Gradient Descent Ascent",
            "url": "https://arxiv.org/abs/2604.03782",
            "listed_date": "2026-04-04",
            "status": "external-reference",
            "id": "forum-0c6c28f9926b40e2"
          },
          {
            "title": "All roads lead to Rome: Path-following Augmented Lagrangian Methods via Bregman Proximal Regularization",
            "url": "https://arxiv.org/abs/2602.15710",
            "listed_date": "2026-02-17",
            "status": "external-reference",
            "id": "forum-7cfeadeb3e6ffe8e"
          },
          {
            "title": "Robust Sublinear Convergence Rates for Iterative Bregman Projections",
            "url": "https://arxiv.org/abs/2602.01372",
            "listed_date": "2026-02-01",
            "status": "external-reference",
            "id": "forum-866aefc0b22d72fe"
          },
          {
            "title": "Trajectory-Wise Certification for Vector-Field Mirror Descent with Deterministic Finite Differences",
            "url": "https://arxiv.org/abs/2602.00634",
            "listed_date": "2026-01-31",
            "status": "external-reference",
            "id": "forum-7b015b9a513dbb3f"
          },
          {
            "title": "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof",
            "url": "https://arxiv.org/abs/2510.23513",
            "listed_date": "2025-10-27",
            "status": "external-reference",
            "id": "forum-7569268f07e889a7"
          }
        ]
      },
      {
        "id": "lower_bounds",
        "title": "AI-Assisted Works on Lower Bounds and Counterexamples",
        "items": [
          {
            "title": "BFGS can converge to non-Clarke-stationary points with positive probability",
            "url": "https://arxiv.org/abs/2610.34087",
            "listed_date": "2026-10-25",
            "status": "external-reference",
            "id": "forum-83e2985bfd8127ad"
          },
          {
            "title": "A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly",
            "url": "https://arxiv.org/abs/2610.28414",
            "listed_date": "2026-10-20",
            "status": "external-reference",
            "id": "forum-c5856efd952cda4b"
          },
          {
            "title": "Tight lower bounds for Lipschitz geodesically convex optimization on hyperbolic space",
            "url": "https://arxiv.org/abs/2610.26815",
            "listed_date": "2026-10-19",
            "status": "external-reference",
            "id": "forum-c0367945cb7623ff"
          },
          {
            "title": "Non-Acceleration of the Heavy-Ball Method in 1D",
            "url": "https://arxiv.org/abs/2610.25104",
            "listed_date": "2026-10-18",
            "status": "external-reference",
            "id": "forum-9b2a90b3605021f5"
          },
          {
            "title": "Strong NP-Hardness of Rank-2 Nonnegative Matrix Factorization",
            "url": "https://arxiv.org/abs/2610.21874",
            "listed_date": "2026-10-15",
            "status": "external-reference",
            "id": "forum-638bcb39ef95591c"
          },
          {
            "title": "On the Complexity of Finding Stationary Points in Stochastic $(L_0, L_1)$-Smooth Nonconvex Optimization",
            "url": "https://arxiv.org/abs/2610.21692",
            "listed_date": "2026-10-15",
            "status": "external-reference",
            "id": "forum-d6ad824a1df23594"
          },
          {
            "title": "Descending Everest with First-Order Oracles: Oracle Complexity of Convex Optimization under $(L_0,L_1)$-Smoothness",
            "url": "https://arxiv.org/abs/2610.21461",
            "listed_date": "2026-10-15",
            "status": "external-reference",
            "id": "forum-a75e737a50c355e8"
          },
          {
            "title": "Does Policy Mirror Descent Converge in Policy with Non-Decomposable Mirror Maps? A Counterexample",
            "url": "https://arxiv.org/abs/2610.19853",
            "listed_date": "2026-10-14",
            "status": "external-reference",
            "id": "forum-94620461bada3867"
          },
          {
            "title": "On the Complexity of Finding Stationary Points of p-th Order Hölder Smooth Functions in One Dimension",
            "url": "https://arxiv.org/abs/2610.16295",
            "listed_date": "2026-10-12",
            "status": "external-reference",
            "id": "forum-4cbed1829ce5eeda"
          },
          {
            "title": "Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets",
            "url": "https://arxiv.org/abs/2610.13590",
            "listed_date": "2026-10-09",
            "status": "external-reference",
            "id": "forum-d9d986f1fbe3330b"
          },
          {
            "title": "Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions",
            "url": "https://arxiv.org/abs/2610.11298",
            "listed_date": "2026-10-08",
            "status": "external-reference",
            "id": "forum-7831aebe8ecfccc6"
          },
          {
            "title": "Stochastic Subgradient Descent at Sharply Repulsive Points: A Bounded Noise Counterexample and Gaussian Noise Avoidance",
            "url": "https://arxiv.org/abs/2610.07777",
            "listed_date": "2026-10-06",
            "status": "external-reference",
            "id": "forum-926cef3e5499ab5a"
          },
          {
            "title": "Near-Optimal Complexity of Finite-Sum Nonconvex-Strongly-Concave Minimax Optimization",
            "url": "https://arxiv.org/abs/2610.04944",
            "listed_date": "2026-10-04",
            "status": "external-reference",
            "id": "forum-19d848ce83dcfee2"
          },
          {
            "title": "Exact counterexamples to R-superlinear convergence of cyclic steepest descent",
            "url": "https://arxiv.org/abs/2610.00939",
            "listed_date": "2026-10-01",
            "status": "external-reference",
            "id": "forum-79374f284540362f"
          },
          {
            "title": "Asymptotic Lower Bounds for Continuous Optimization",
            "url": "https://arxiv.org/abs/2609.34303",
            "listed_date": "2026-09-28",
            "status": "external-reference",
            "id": "forum-e367ca0f9d85a1df"
          },
          {
            "title": "No Universal Remainder Rate for Chambolle-Dossal Acceleration",
            "url": "https://arxiv.org/abs/2609.31557",
            "listed_date": "2026-09-25",
            "status": "external-reference",
            "id": "forum-8777fc9d0662e62a"
          },
          {
            "title": "Silver Rate Is (Almost) Optimal for Gradient Descent: The Strongly Convex Case",
            "url": "https://arxiv.org/abs/2609.26873",
            "listed_date": "2026-09-22",
            "status": "external-reference",
            "id": "forum-b70297b0f5ce01c1"
          },
          {
            "title": "An $Ω(κ_y^8ε^{-6})$ Lower Bound for Stochastic NC-SC Bilevel Optimization with First-order Oracles",
            "url": "https://arxiv.org/abs/2609.21905",
            "listed_date": "2026-09-18",
            "status": "external-reference",
            "id": "forum-55ca033680988ec1"
          },
          {
            "title": "Bounds on the Semidefinite Programming Complexity of the Euclidean Ball",
            "url": "https://arxiv.org/abs/2609.21089",
            "listed_date": "2026-09-17",
            "status": "external-reference",
            "id": "forum-eddb85fd209fca7e"
          },
          {
            "title": "The Complexity of Finding Stationary Points in Nonsmooth Nonconvex Optimization",
            "url": "https://arxiv.org/abs/2609.17780",
            "listed_date": "2026-09-15",
            "status": "external-reference",
            "id": "forum-243bf5e02165d1b0"
          },
          {
            "title": "Optimal Deterministic First-Order Oracle Complexity for Nonconvex-Concave Minimax Optimization",
            "url": "https://arxiv.org/abs/2609.14235",
            "listed_date": "2026-09-13",
            "status": "external-reference",
            "id": "forum-bacab5dfaf6fa4ff"
          },
          {
            "title": "Lower Bounds for Nonconvex-Concave Minimax Optimization",
            "url": "https://arxiv.org/abs/2609.14233",
            "listed_date": "2026-09-13",
            "status": "external-reference",
            "id": "forum-5cba6bfa5440be45"
          },
          {
            "title": "A Two-Dimensional Extremizer for Relatively Inexact Gradient Descent",
            "url": "https://arxiv.org/abs/2610.00156",
            "listed_date": "2026-09-11",
            "status": "external-reference",
            "id": "forum-557c7d8d777283db"
          },
          {
            "title": "Sharpness and Rigidity of the Two-Factor Recht-Re Lower Bound",
            "url": "https://arxiv.org/abs/2610.00155",
            "listed_date": "2026-09-11",
            "status": "external-reference",
            "id": "forum-bf6f6c576f0c9d88"
          },
          {
            "title": "A Simple Complexity Lower Bound for Solving $Ax=b$",
            "url": "https://arxiv.org/abs/2609.10874",
            "listed_date": "2026-09-09",
            "status": "external-reference",
            "id": "forum-cd02d5efb19469f8"
          },
          {
            "title": "Silver Rate Is (Almost) Optimal for Gradient Descent",
            "url": "https://arxiv.org/abs/2609.09152",
            "listed_date": "2026-09-08",
            "status": "external-reference",
            "id": "forum-d14cc888a039bab4"
          },
          {
            "title": "Stronger Lower Bounds for (Non-)Anytime Acceleration of Gradient Descent",
            "url": "https://arxiv.org/abs/2609.04032",
            "listed_date": "2026-09-03",
            "status": "external-reference",
            "id": "forum-3068cfb219fcbe93"
          },
          {
            "title": "Improved Gradient Descent Lower Bounds Beyond Nesterov",
            "url": "https://arxiv.org/abs/2609.02855",
            "listed_date": "2026-09-02",
            "status": "external-reference",
            "id": "forum-0ba2d1df64333d39"
          },
          {
            "title": "A Mini-Batch Counterexample to Last-Iterate Convergence in Definable Optimization",
            "url": "https://arxiv.org/abs/2608.19074",
            "listed_date": "2026-08-19",
            "status": "external-reference",
            "id": "forum-28a8a7d577b1e20c"
          },
          {
            "title": "ADMM Fails to Achieve an $O(K^{-1})$ Ergodic KKT Residual Bound",
            "url": "https://arxiv.org/abs/2608.16610",
            "listed_date": "2026-08-17",
            "status": "external-reference",
            "id": "forum-ac325fd7ef72bbcf"
          },
          {
            "title": "AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block",
            "url": "https://arxiv.org/abs/2608.14396",
            "listed_date": "2026-08-14",
            "status": "external-reference",
            "id": "forum-590388e537f3aed3"
          },
          {
            "title": "A lower bound for stepsize-based acceleration of gradient descent",
            "url": "https://arxiv.org/abs/2608.10418",
            "listed_date": "2026-08-11",
            "status": "external-reference",
            "id": "forum-ceb658ad521b16f0"
          },
          {
            "title": "A Tight Lower Bound for Smooth Nonconvex Stochastic Optimization with Bounded Gradient Noise",
            "url": "https://arxiv.org/abs/2608.09004",
            "listed_date": "2026-08-10",
            "status": "external-reference",
            "id": "forum-521b62671aa503d1"
          },
          {
            "title": "The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity",
            "url": "https://arxiv.org/abs/2608.06719",
            "listed_date": "2026-08-07",
            "status": "external-reference",
            "id": "forum-bd9e678aeddbf861"
          },
          {
            "title": "On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations",
            "url": "https://arxiv.org/abs/2608.04607",
            "listed_date": "2026-08-05",
            "status": "external-reference",
            "id": "forum-4f167a4f366acef6"
          },
          {
            "title": "A Counterexample to Fourier Alignment in Single-Neuron Modular Addition",
            "url": "https://arxiv.org/abs/2608.04451",
            "listed_date": "2026-08-05",
            "status": "external-reference",
            "id": "forum-435456b6791a6816"
          },
          {
            "title": "Optimal Deterministic Oracle Complexity for Weakly Convex Optimization",
            "url": "https://arxiv.org/abs/2608.03246",
            "listed_date": "2026-08-04",
            "status": "external-reference",
            "id": "forum-dff6060c9aa7b6bf"
          },
          {
            "title": "Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\\geq 4$",
            "url": "https://arxiv.org/abs/2607.21579",
            "listed_date": "2026-07-23",
            "status": "external-reference",
            "id": "forum-678b51f578199efc"
          },
          {
            "title": "Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values",
            "url": "https://arxiv.org/abs/2607.13335",
            "listed_date": "2026-07-14",
            "status": "external-reference",
            "id": "forum-0b69f08dcd3e2dfe"
          },
          {
            "title": "A Resolution of the SS--RS--GD Inequalities",
            "url": "https://arxiv.org/abs/2607.22620",
            "listed_date": "2026-06-16",
            "status": "external-reference",
            "id": "forum-b07582b1b70ad798"
          },
          {
            "title": "Cesàro means of firmly nonexpansive iterates need not converge strongly",
            "url": "https://arxiv.org/abs/2605.25491",
            "listed_date": "2026-05-25",
            "status": "external-reference",
            "id": "forum-e508a7f488a9a454"
          },
          {
            "title": "Curvature-Dependent Lower Bounds for Frank-Wolfe",
            "url": "https://arxiv.org/abs/2605.10595",
            "listed_date": "2026-05-11",
            "status": "external-reference",
            "id": "forum-39b6f708bc68fdf0"
          },
          {
            "title": "Complexity of Classical Acceleration for $\\ell_1$-Regularized PageRank",
            "url": "https://arxiv.org/abs/2602.21138",
            "listed_date": "2026-02-24",
            "status": "external-reference",
            "id": "forum-bbfc4c925b310111"
          }
        ]
      }
    ]
  },
  "optlib": {
    "repository": "https://github.com/optsuite/optlib",
    "commit": "5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3",
    "license": "Apache-2.0",
    "license_sha256": "69849221bfb90053de2134ef5e6d540287b4b98062326492f1f96f5da685524b",
    "copyright": "2026 Chenyi Li, Zichen Wang, Ziyu Wang, Zaiwen Wen; retained upstream, not transferred to Samplinglib.",
    "readme_sha256": "64a17c5e9cfe2f658a904f0a3a0db7431611d90bbb1347755ccbc0e3cbec7e55",
    "toolchain": "leanprover/lean4:v4.13.0",
    "integration": "External reference/port source only; existing ASTIS matches are linked from canonical lessons.",
    "modules": [
      {
        "path": "Optlib/Algorithm.lean",
        "git_blob": "1f5852f3c1c5a3df0f3fde70de8fc70ff3196459",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/ADMM/Inv_bounded.lean",
        "git_blob": "827677e1b1d0d3385a51ea1e4b60c25c631bf7eb",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/ADMM/Inv_bounded.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/ADMM/Lemma.lean",
        "git_blob": "e02d256c59e8516ebc7d0feae68c6ba865f42235",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/ADMM/Lemma.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/ADMM/Scheme.lean",
        "git_blob": "3eda488c02a37a84cc75cca02f6a85d853bfb5e2",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/ADMM/Scheme.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/ADMM/Theroem_converge.lean",
        "git_blob": "d432b56c69fee3df1887ed45081542deeefe70cf",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/ADMM/Theroem_converge.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/BCD/Convergence.lean",
        "git_blob": "35be56085e7cc16440977e730ea01fd8f702c930",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/BCD/Convergence.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/BCD/Scheme.lean",
        "git_blob": "acc653986829844f11a291559c701bab89c05661",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/BCD/Scheme.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/GD/GradientDescent.lean",
        "git_blob": "04590cfd05db51d24cc30224aec0572c74b35526",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/GD/GradientDescent.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/GD/GradientDescentStronglyConvex.lean",
        "git_blob": "d4cd46e5f6acc9b13ae6c32c880e484e30e621b0",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/GD/GradientDescentStronglyConvex.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/LASSO.lean",
        "git_blob": "9e9dc6459cd14ad01dd8cccf52aa966bcf714309",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/LASSO.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/Nesterov/NesterovAccelerationFirst.lean",
        "git_blob": "794055ea384c9a1408dd5b27de5627433198d651",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/Nesterov/NesterovAccelerationFirst.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/Nesterov/NesterovAccelerationSecond.lean",
        "git_blob": "052e3156575b1d243a748cd118fa77b044b3f5a3",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/Nesterov/NesterovAccelerationSecond.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/Nesterov/NesterovSmooth.lean",
        "git_blob": "5b3fda266851004400639e3c9bb4bf6ffaab45bf",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/Nesterov/NesterovSmooth.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/ProximalGradient.lean",
        "git_blob": "51d60d21be199b833a25efdf72fca8c761412801",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/ProximalGradient.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Algorithm/SubgradientMethod.lean",
        "git_blob": "71509655ca7def5d183775b8d99e23ce7dec81c4",
        "area": "Algorithm",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Algorithm/SubgradientMethod.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex.lean",
        "git_blob": "929ac847b6142ffc52b8382e1faa1135267663cf",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/BanachSubgradient.lean",
        "git_blob": "307744882431c0d5bbfaa309a9a0123eb1af7058",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/BanachSubgradient.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/ClosedCone.lean",
        "git_blob": "263f7059d8dd0a2871452e3fbf371174f9d8d12b",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/ClosedCone.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/ConicCaratheodory.lean",
        "git_blob": "9f6bf217da4782e850f80f814d69a3ae709d618a",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/ConicCaratheodory.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/ConvexFunction.lean",
        "git_blob": "378e2ebb6e6245c9628b6793e0e9e665b6e14e28",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/ConvexFunction.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/Farkas.lean",
        "git_blob": "38db9b1a60f615207b9b511d17bd30919f62e42c",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/Farkas.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/FiniteDimensionalConvexFunctionsLocallyLipschitz.lean",
        "git_blob": "5e90ea40eef6bd3cceae44cb34e9f2e5598ade8d",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/FiniteDimensionalConvexFunctionsLocallyLipschitz.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/ImageSubgradientClosed.lean",
        "git_blob": "e0bb3d282c97e39824866371f2404fd435a36ca5",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/ImageSubgradientClosed.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/QuasiConvexFirstOrder.lean",
        "git_blob": "e1db12aae4c6bad2822f1391b77242a0e65bb084",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/QuasiConvexFirstOrder.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/StronglyConvex.lean",
        "git_blob": "c36d40ed6cfd411b017bbdcd35459720798e2cd1",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/StronglyConvex.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Convex/Subgradient.lean",
        "git_blob": "c9c48f2578a15972e47eb01e43aa66a351e5e987",
        "area": "Convex",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Convex/Subgradient.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Differential.lean",
        "git_blob": "86ec7bbe8aafe9237541aa8b1e8520c72f4d4bd7",
        "area": "Differential",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Differential.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Differential/Calculation.lean",
        "git_blob": "89e163eb4000154e898b47273939ebd875f80718",
        "area": "Differential",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Differential/Calculation.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Differential/GradientDiv.lean",
        "git_blob": "57ad10f14b2ae3f8c7a6bf3f0609f1adc0d01a72",
        "area": "Differential",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Differential/GradientDiv.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Differential/Lemmas.lean",
        "git_blob": "a8f3203066d8b014290c5c2f4b9987dd234f2bf9",
        "area": "Differential",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Differential/Lemmas.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Differential/Subdifferential.lean",
        "git_blob": "4a67cea5346b3aca245af1448f97abfb4f2deda7",
        "area": "Differential",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Differential/Subdifferential.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Function.lean",
        "git_blob": "31897021eabc7bb3f6f2a82f6f602ff84906e0ef",
        "area": "Function",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Function.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Function/KL.lean",
        "git_blob": "f2f0c1a47b2907b9b8d41248ce6352bde4c00b53",
        "area": "Function",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Function/KL.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Function/L1Space.lean",
        "git_blob": "d3d04369c84d9d4836a7d7477a69c22bbb2ad93f",
        "area": "Function",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Function/L1Space.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Function/Lsmooth.lean",
        "git_blob": "1ff68dd4686543513c417410adce1911d97ad4c0",
        "area": "Function",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Function/Lsmooth.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Function/MinimaClosedFunction.lean",
        "git_blob": "44c01dc43b52d7c79a559f1a32caf9ba2dbd1c40",
        "area": "Function",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Function/MinimaClosedFunction.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Function/Proximal.lean",
        "git_blob": "2ad865f19d45ff87f0fc0e1d8a2b15243715701a",
        "area": "Function",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Function/Proximal.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Optimality.lean",
        "git_blob": "0c8de6a7c790978d404d49fe84b86ce2f653aedf",
        "area": "Optimality",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Optimality.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Optimality/Constrained_Problem.lean",
        "git_blob": "03cba1d4a928098071cf4a2f92a92ab9ed5e5073",
        "area": "Optimality",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Optimality/Constrained_Problem.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Optimality/OptimalityConditionOfUnconstrainedProblem.lean",
        "git_blob": "757ec1ee999dc3965f82a6fe280f9515bafe864c",
        "area": "Optimality",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Optimality/OptimalityConditionOfUnconstrainedProblem.lean",
        "status": "external-reference"
      },
      {
        "path": "Optlib/Optimality/Weak_Duality.lean",
        "git_blob": "4be2b672561cb2cbb8ceeed7ac4db8d44195ee3d",
        "area": "Optimality",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/Optlib/Optimality/Weak_Duality.lean",
        "status": "external-reference"
      }
    ],
    "readme_resources": [
      {
        "section": "Code Explanations",
        "topic": "Differential",
        "title": "Basic.lean",
        "url": "https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Analysis/Calculus/Gradient/Basic.lean",
        "status": "external-reference"
      },
      {
        "section": "Code Explanations",
        "topic": "Convex",
        "title": "Strong.lean (upstream migration reference)",
        "url": "https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Analysis/Convex/Strong.lean",
        "status": "external-reference"
      },
      {
        "section": "Code Explanations",
        "topic": "Function",
        "title": "ClosedFunction.lean",
        "url": "https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Topology/Semicontinuous.lean",
        "status": "external-reference"
      },
      {
        "section": "Topics",
        "topic": "Convex Analysis",
        "title": "Convex Analysis (R. T. Rockafellar)",
        "url": "https://press.princeton.edu/books/paperback/9780691015866/convex-analysis",
        "status": "external-reference"
      },
      {
        "section": "Topics",
        "topic": "Nonlinear Programming",
        "title": "Numerical Optimization (Jorge Nocedal, Stephen J. Wright)",
        "url": "https://link.springer.com/book/10.1007/978-0-387-40065-5",
        "status": "external-reference"
      },
      {
        "section": "Topics",
        "topic": "Nonlinear Programming",
        "title": "Optimization: Modeling, Algorithm and Theory",
        "url": "http://faculty.bicmr.pku.edu.cn/~wenzw/optbook.html",
        "status": "external-reference"
      },
      {
        "section": "Topics",
        "topic": "Integer Programming",
        "title": "Integer Programming (Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli)",
        "url": "https://link.springer.com/book/10.1007/978-3-319-11008-0",
        "status": "external-reference"
      },
      {
        "section": "Topics",
        "topic": "Numerical Linear Algebra",
        "title": "Matrix Computations (Golub & Van Loan)",
        "url": "https://epubs.siam.org/doi/abs/10.1137/1.9781421407944",
        "status": "external-reference"
      },
      {
        "section": "Topics",
        "topic": "High Dimensional Probability",
        "title": "High-Dimensional Probability (Roman Vershynin)",
        "url": "https://www.math.uci.edu/~rvershyn/teaching/hdp/hdp.html",
        "status": "external-reference"
      },
      {
        "section": "Lean Projects",
        "topic": "Formalization Platform",
        "title": "ReasLab",
        "url": "https://reaslab.io",
        "status": "external-reference"
      },
      {
        "section": "Lean Projects",
        "topic": "Formalization Projects",
        "title": "Optlib",
        "url": "https://github.com/optsuite/optlib",
        "status": "external-reference"
      },
      {
        "section": "Lean Projects",
        "topic": "Formalization Projects",
        "title": "ReasBook",
        "url": "https://github.com/optpku/ReasBook",
        "status": "external-reference"
      },
      {
        "section": "Lean Projects",
        "topic": "Benchmark",
        "title": "AMBER",
        "url": "https://github.com/optsuite/AMBER",
        "status": "external-reference"
      },
      {
        "section": "Lean Projects",
        "topic": "Autoformalization and Theorem Proving Systems",
        "title": "M2F",
        "url": "https://github.com/optsuite/M2F",
        "status": "external-reference"
      },
      {
        "section": "Lean Projects",
        "topic": "Autoformalization and Theorem Proving Systems",
        "title": "SITA",
        "url": "https://github.com/chenyili0818/SITA",
        "status": "external-reference"
      },
      {
        "section": "Lean Projects",
        "topic": "Autoformalization and Theorem Proving Systems",
        "title": "lean-tools-mcp",
        "url": "https://github.com/optsuite/lean-tools-mcp",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Formalization of Optimization, Numerical Linear Algebra",
        "title": "Wanli Ma, Zichen Wang, Zaiwen Wen, *A Unified Framework for Formalizing Matrix Decomposition Proofs*.",
        "url": "https://arxiv.org/abs/2607.05874",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Formalization of Optimization, Numerical Linear Algebra",
        "title": "Chenyi Li, Ziyu Wang, Wanyi He, Yuxuan Wu, Shengyang Xu, Zaiwen Wen. Formalization of Complexity Analysis of the First-order Optimization Algorithms, Journal of Automated Reasoning",
        "url": "https://arxiv.org/abs/2403.11437",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Formalization of Optimization, Numerical Linear Algebra",
        "title": "Chenyi Li, Zichen Wang, Yifan Bai, Yunxi Duan, Yuqing Gao, Pengfei Hao, Zaiwen Wen, Formalization of Algorithms for Optimization with Block Structures, Science in China Series A: Mathematics",
        "url": "http://arxiv.org/abs/2503.18806",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Formalization of Optimization, Numerical Linear Algebra",
        "title": "Chenyi Li, Shengyang Xu, Chumin Sun, Li Zhou, Zaiwen Wen, Formalization of Optimality Conditions for Smooth Constrained Optimization Problems",
        "url": "https://arxiv.org/abs/2503.18821",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Formalization of Optimization, Numerical Linear Algebra",
        "title": "Chenyi Li, Zaiwen Wen, An Introduction to Mathematics Formalization Based on Lean (in Chinese",
        "url": "http://faculty.bicmr.pku.edu.cn/~wenzw/paper/OptLean.pdf",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Autoformalization and Automatic Theorem Proving",
        "title": "Ziyu Wang, Bowen Yang, Chenyi Li, Yuan Zhang, Shihao Zhou, Bin Dong, Zaiwen Wen, Translating Informal Proofs into Formal Proofs Using a Chain of States",
        "url": "https://arxiv.org/abs/2512.10317",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Autoformalization and Automatic Theorem Proving",
        "title": "Chenyi Li, Wanli Ma, Zichen Wang, Zaiwen Wen, SITA: A Framework for Structure-to-Instance Theorem Autoformalization, AAAI, 2026",
        "url": "https://arxiv.org/abs/2511.10356",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Autoformalization and Automatic Theorem Proving",
        "title": "Chenyi Li, Yanchen Nie, Zhenyu Ming, Gong Zhang, Kun Yuan, Zaiwen Wen, OptProver: Bridging Olympiad and Optimization through Continual Training in Formal Theorem Proving",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/README.md#publications",
        "link_note": "Upstream lists this title without a paper URL; link opens its README citation, not an inferred manuscript.",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Autoformalization and Automatic Theorem Proving",
        "title": "Zichen Wang, Wanli Ma, Zhenyu Ming, Gong Zhang, Kun Yuan, Zaiwen Wen, M2F: Automated Formalization of Mathematical Literature at Scale",
        "url": "https://arxiv.org/abs/2602.17016",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Premise Selection",
        "title": "Zichen Wang, Anjie Dong, Zaiwen Wen, Tree-Based Premise Selection for Lean4, Nips, 2025",
        "url": "https://neurips.cc/virtual/2025/loc/san-diego/poster/116011",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Premise Selection",
        "title": "Shu Miao, Zichen Wang, Anjie Dong, Yishan Wu, Weixi Zhang, Zaiwen Wen, Directed Multi-Relational GCNs for Premise Selection",
        "url": "https://github.com/optsuite/optlib/blob/5da27c5f95aa6a8a45b8c14b968ade4c13ff18c3/README.md#publications",
        "link_note": "Upstream lists this title without a paper URL; link opens its README citation, not an inferred manuscript.",
        "status": "external-reference"
      },
      {
        "section": "Publications",
        "topic": "Benchmark",
        "title": "Bowen Yang, Yi Yuan, Chenyi Li, Ziyu Wang, Liangqi Li, Bo Zhang, Zhe Li, Zaiwen Wen, Construction–Verification: A Benchmark for Formalizing Applied Mathematics in Lean 4",
        "url": "https://arxiv.org/abs/2602.01291",
        "status": "external-reference"
      },
      {
        "section": "References",
        "topic": "",
        "title": "H. Liu, J. Hu, Y. Li, Z. Wen, Optimization: Modeling, Algorithm and Theory (in Chinese)",
        "url": "http://faculty.bicmr.pku.edu.cn/~wenzw/optbook.html",
        "status": "external-reference"
      },
      {
        "section": "References",
        "topic": "",
        "title": "Rockafellar, R. Tyrrell, and Roger J-B. Wets. Variational analysis. Vol. 317. Springer Science & Business Media, 2009.",
        "url": "https://link.springer.com/book/10.1007/978-3-642-02431-3",
        "status": "external-reference"
      },
      {
        "section": "References",
        "topic": "",
        "title": "Nocedal, Jorge, and Stephen J. Wright, eds. Numerical optimization. New York, NY: Springer New York, 1999.",
        "url": "https://link.springer.com/chapter/10.1007/0-387-22742-3_18",
        "status": "external-reference"
      },
      {
        "section": "References",
        "topic": "",
        "title": "Nesterov, Yurii. Lectures on convex optimization. Vol. 137. Berlin: Springer, 2018.",
        "url": "https://link.springer.com/book/10.1007/978-3-319-91578-4",
        "status": "external-reference"
      },
      {
        "section": "References",
        "topic": "",
        "title": "Convex Analysis, Vol. 28 of Princeton Math. Series, Princeton Univ. Press, 1970",
        "url": "https://press.princeton.edu/books/paperback/9780691015866/convex-analysis",
        "status": "external-reference"
      },
      {
        "section": "References",
        "topic": "",
        "title": "Bolte, J., Sabach, S. & Teboulle, M. Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146, 459–494 (2014).",
        "url": "https://link.springer.com/article/10.1007/s10107-013-0701-9",
        "status": "external-reference"
      },
      {
        "section": "References",
        "topic": "",
        "title": "Maryam Fazel, Ting Kei Pong, Defeng Sun, and Paul Tseng. Hankel matrix rank minimization with applications to system identification and realization. SIAM Journal on Matrix Analysis and Applications, 34(3):946–977, 2013",
        "url": "https://epubs.siam.org/doi/abs/10.1137/110853996",
        "status": "external-reference"
      }
    ]
  }
}
