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AI-Assisted Works on Lower Bounds and Counterexamples
A complete source-listed bibliography; choose a title, then inspect the primary source before using its mathematical claims.
43 references. Dates are supplied by the Forum, not independently verified publication dates.
- BFGS can converge to non-Clarke-stationary points with positive probability external reference
- A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly external reference
- Tight lower bounds for Lipschitz geodesically convex optimization on hyperbolic space external reference
- Non-Acceleration of the Heavy-Ball Method in 1D external reference
- Strong NP-Hardness of Rank-2 Nonnegative Matrix Factorization external reference
- On the Complexity of Finding Stationary Points in Stochastic \((L_0, L_1)\)-Smooth Nonconvex Optimization external reference
- Descending Everest with First-Order Oracles: Oracle Complexity of Convex Optimization under \((L_0,L_1)\)-Smoothness external reference
- Does Policy Mirror Descent Converge in Policy with Non-Decomposable Mirror Maps? A Counterexample external reference
- On the Complexity of Finding Stationary Points of p-th Order Hölder Smooth Functions in One Dimension external reference
- Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets external reference
- Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions external reference
- Stochastic Subgradient Descent at Sharply Repulsive Points: A Bounded Noise Counterexample and Gaussian Noise Avoidance external reference
- Near-Optimal Complexity of Finite-Sum Nonconvex-Strongly-Concave Minimax Optimization external reference
- Exact counterexamples to R-superlinear convergence of cyclic steepest descent external reference
- Asymptotic Lower Bounds for Continuous Optimization external reference
- No Universal Remainder Rate for Chambolle-Dossal Acceleration external reference
- Silver Rate Is (Almost) Optimal for Gradient Descent: The Strongly Convex Case external reference
- An \(Ω(κ_y^8ε^{-6})\) Lower Bound for Stochastic NC-SC Bilevel Optimization with First-order Oracles external reference
- Bounds on the Semidefinite Programming Complexity of the Euclidean Ball external reference
- The Complexity of Finding Stationary Points in Nonsmooth Nonconvex Optimization external reference
- Optimal Deterministic First-Order Oracle Complexity for Nonconvex-Concave Minimax Optimization external reference
- Lower Bounds for Nonconvex-Concave Minimax Optimization external reference
- A Two-Dimensional Extremizer for Relatively Inexact Gradient Descent external reference
- Sharpness and Rigidity of the Two-Factor Recht-Re Lower Bound external reference
- A Simple Complexity Lower Bound for Solving \(Ax=b\) external reference
- Silver Rate Is (Almost) Optimal for Gradient Descent external reference
- Stronger Lower Bounds for (Non-)Anytime Acceleration of Gradient Descent external reference
- Improved Gradient Descent Lower Bounds Beyond Nesterov external reference
- A Mini-Batch Counterexample to Last-Iterate Convergence in Definable Optimization external reference
- ADMM Fails to Achieve an \(O(K^{-1})\) Ergodic KKT Residual Bound external reference
- AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block external reference
- A lower bound for stepsize-based acceleration of gradient descent external reference
- A Tight Lower Bound for Smooth Nonconvex Stochastic Optimization with Bounded Gradient Noise external reference
- The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity external reference
- On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations external reference
- A Counterexample to Fourier Alignment in Single-Neuron Modular Addition external reference
- Optimal Deterministic Oracle Complexity for Weakly Convex Optimization external reference
- Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension \(n\geq 4\) external reference
- Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values external reference
- A Resolution of the SS--RS--GD Inequalities external reference
- Cesàro means of firmly nonexpansive iterates need not converge strongly external reference
- Curvature-Dependent Lower Bounds for Frank-Wolfe external reference
- Complexity of Classical Acceleration for \(\ell_1\)-Regularized PageRank external reference