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Table of Contents

  1. AI-Driven Optimization Research
  2. Formal Verification
  3. Optimization Education
  4. AI-Assisted Works on Optimization Modeling
  5. AI-Assisted Works on Algorithm Design and Analysis
  6. AI-Assisted Works on Lower Bounds and Counterexamples

AI-Driven Optimization Research

  1. Peppy: An AI-Assisted Workflow for Tight Convergence Analysis of Optimization Algorithms (Sep 28, 2026)
  2. Auditing Optimization Papers with Agentic AI (Aug 24, 2026)
  3. A Domain-Specific Harness for End-to-End Automation of Optimization Research (Aug 7, 2026)
  4. Advancing Mathematics Research with AI-Driven Formal Proof Search (May 21, 2026)
  5. ImprovEvolve: Basin-Hopping Meets LLM-Guided Evolutionary Search (Feb 10, 2026)
  6. AI and the future of optimization modeling (Oct 21, 2024)
  7. OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale (Jun 29, 2024)
  8. OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models (Feb 15, 2024)
  9. Guiding RL Agents with Classical Algorithms and Heuristics to Solve Combinatorial Optimization Problems on Graphs (Sep 23, 2023)

Formal Verification

  1. Optlib

Optimization Education

  1. Open Problems as Active Learning in the Age of AI (Sep 15, 2026)

AI-Assisted Works on Optimization Modeling

  1. Computing Multi-Slot First-Price Pacing Equilibria at Scale via Entropic Smoothing (Oct 16, 2026)
  2. Are Single-Leader-Multi-Follower Problems Particular Cases of Bilevel Optimization? (Oct 16, 2026)
  3. Utility-Based Recovery Risk Measures: Redundancy and Approximation for Portfolio Optimization (Oct 9, 2026)
  4. The Geometry of Anisotropic Dilation for Optimal Regularization (Oct 7, 2026)
  5. Sliced Wasserstein Barycenters: The Analysis Approach within the Barycentric Coding Model in the Wasserstein Space (Oct 6, 2026)
  6. More on Disjunctive Convex Hulls of Generalized Cross Polytopes (Oct 4, 2026)
  7. Volumes of the strong and weak relaxations of the uncapacitated facility-location polytope (Sep 22, 2026)
  8. Quadratic Convexification of a Square Truncated by a Hyperbola (Aug 27, 2026)
  9. Joint-Range Inequalities for Nonconvex QCQPs (Aug 4, 2026)
  10. Composition and tensor train structure in polynomial optimization (Apr 19, 2026)
  11. Semidefinite relaxations for nonlinear elasticity with energies convex in the Cauchy-Green strain tensor (Apr 15, 2026)
  12. Polyconvexity with Moments and Sums of Squares (Apr 13, 2026)

AI-Assisted Works on Algorithm Design and Analysis

  1. DREAM: Delay-Resistant Acceleration with Momentum (Oct 27, 2026)
  2. Continuous-time analysis and algorithms for linear and convex quadratic programs via exactly solvable differential inclusions (Oct 21, 2026)
  3. A short proof of a range-relative FPTAS for polynomial integer optimization over bounded polyhedra (Oct 21, 2026)
  4. Weak-$L^α$ Noise, Strong Guarantees: Gradient Clipping under Affine Heavy Tails (Oct 20, 2026)
  5. Gradient descent reaches arbitrary accuracy in a fixed number of large steps on multiclass logistic regression (Oct 19, 2026)
  6. On the Nonoccurrence of Gradient Restart in Nesterov Accelerated Gradient Method (Oct 19, 2026)
  7. Acceleration of Generalized Conditional Gradient Methods (Oct 18, 2026)
  8. Accelerating Finite-Sum Bilevel Optimization with Fully First-Order Oracles (Oct 17, 2026)
  9. Optimal degree bounds for sum-of-squares representations (Oct 17, 2026)
  10. Convergence Rates for Lasserre's Upper-Bound Hierarchy on $\mathbb{R}^d$ with Gaussian Measure (Oct 15, 2026)
  11. Envelope Cubic Regularized Newton Method for Nonconvex-Strongly-Concave Minimax Optimization (Oct 14, 2026)
  12. First-order Optimization Methods with Generalized Smoothness for Low-rank Matrix Factorization (Oct 13, 2026)
  13. Cyclic steepest descent is $R$-superlinearly convergent for almost every initialization on two-spectrum quadratics (Oct 11, 2026)
  14. Adaptive two-points zero-order accelerated methods for stochastic convex optimization problems (Oct 10, 2026)
  15. The exact worst-case asymptotic rate of Nesterov acceleration for strongly convex optimization (Oct 10, 2026)
  16. Optimal Algorithms for Nonsmooth Nonconvex Stochastic Optimization with Constraints (Oct 9, 2026)
  17. Matching the Lower Bounds: Stochastic Contracting Cubic Newton and Its Optimal Acceleration (Oct 8, 2026)
  18. Accelerated Proximal Gradient Method for Non-Strongly Convex Time-Varying Optimization (Oct 8, 2026)
  19. SDDP has polynomial iteration complexity in the horizon (Oct 8, 2026)
  20. Polynomial Acceleration of Alternating Projections: Chebyshev Acceleration, Convergence Rates, and Retractions (Oct 5, 2026)
  21. Optimal Oracle Complexity for Finite-Sum Monotone Inclusions (Oct 4, 2026)
  22. Finding Stationary Points under Higher-Order Smoothness: Trapping Algorithms and First-Order Lower Bounds (Oct 2, 2026)
  23. Boundary Geometry and Global Rates of Cyclic Coordinate Descent for SVM Duals (Sep 30, 2026)
  24. Acceleration for Affine-coupling problems (Sep 29, 2026)
  25. Greedy sign-based box splitting: exact solvable classes, sharp thresholds and order-oracle complexity (Sep 29, 2026)
  26. Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding (Sep 28, 2026)
  27. Accelerated Algorithms for Stochastic Monotone Inclusions with Fixed Queries (Sep 28, 2026)
  28. Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memory (Sep 27, 2026)
  29. AltGDA Achieves Global $O(1/T)$ Ergodic Convergence in Matrix Games (Sep 26, 2026)
  30. Anchored Extra-Proximal Methods: Optimal Higher-Order Methods for Monotone Inclusion Problems (Sep 24, 2026)
  31. Optimal High-Order Methods for Solving Monotone Variational Inequalities (Sep 20, 2026)
  32. Moving-Average Iteration of Linear Maps (Sep 18, 2026)
  33. Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates (Sep 17, 2026)
  34. The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings (Sep 17, 2026)
  35. Bounded Integer Quadratic Programming through Parallelepiped Covers and Discrete Convic Optimization (Sep 15, 2026)
  36. Optimal Recursive Composition and Dyadic Phase Laws for Gradient Descent with Predetermined Stepsizes (Sep 10, 2026)
  37. Constant Steps Are s-Composable: An Exact Interpolation Certificate for Gradient Descent (Sep 10, 2026)
  38. Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth (Sep 10, 2026)
  39. An $O(1/T^3)$ algorithm for minimizing convex quadratic functions over the $L_1$ ball (Sep 9, 2026)
  40. Heavy-Ball Method under Randomized Schedules (Sep 9, 2026)
  41. The Exact Time-Uniform Rate Frontier for Stochastic Gradient Descent on Smooth Convex Objectives (Sep 8, 2026)
  42. On Minimax Optimality and Uniqueness of Fixed-Step First-Order Methods for Smooth Convex Optimization (Sep 7, 2026)
  43. Centered Permutation Prefixes for SGD with Random Reshuffling: Sharp Rates, Hölder Geometry, and Composite Proximal Extensions (Sep 4, 2026)
  44. Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman--Pereira Matrices (Sep 1, 2026)
  45. Optimal Parameter-Free Gradient Minimization in $\ell_p$ Geometry (Aug 27, 2026)
  46. When a Relaxed PEP Is Exact: The Sharp Queried-Gradient Rate of Nesterov's Fast Gradient Method (Aug 27, 2026)
  47. Zeroth-Order Nonsmooth Nonconvex Optimization with Convex Liftings and Its Application to State-Feedback $H_\infty$ Policy Optimization (Aug 24, 2026)
  48. Doubling the dimension yields a benign landscape for the squared-stress (Aug 17, 2026)
  49. On the Complexity of BFGS Method for Smooth Convex Optimization (Aug 17, 2026)
  50. Radial-type error bounds for semidefinite feasibility problems without strict feasibility: qualitative estimates and asymptotic tightness (Aug 10, 2026)
  51. Halpern Iteration Achieves $\tilde{\mathcal{O}}(ε^{-1/p})$ $p$th-Order Oracle Complexity for Monotone Variational Inequalities (Aug 9, 2026)
  52. Forward-Reflected-Backward algorithm with Linesearch (Jul 22, 2026)
  53. Improved Convergence Rate for Stochastic Multi-Gradient Descent: A Proof Discovered with AI (Jul 20, 2026)
  54. From Manifold Identification to Newton Acceleration on Intersections: Sparse Stiefel Optimization (Jul 14, 2026)
  55. Sharp $O(1/k)$ convergence rate for the Sinkhorn algorithm via a local analysis (Jun 27, 2026)
  56. Accelerated and Stable Convergence with Anchored Generalized Optimistic Method (Jun 19, 2026)
  57. Unified Ergodic Primal-Dual Gap Rates with Unhalved Primal Stepsizes (Jun 19, 2026)
  58. Last-Iterate Convergence of Optimistic Multiplicative Weight Update (Jun 10, 2026)
  59. Accelerating Min-Max Optimization via Power-Law Stepsizes (Jun 1, 2026)
  60. Efficient Gradient Methods for Distributed Saddle Problems (May 18, 2026)
  61. Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case (Apr 29, 2026)
  62. Boţ-Nguyen Acceleration, Weighted Mean Ergodic Iteration, and the Beta-Binomial Distribution (Apr 18, 2026)
  63. An Improved Last-Iterate Convergence Rate for Anchored Gradient Descent Ascent (Apr 4, 2026)
  64. All roads lead to Rome: Path-following Augmented Lagrangian Methods via Bregman Proximal Regularization (Feb 17, 2026)
  65. Robust Sublinear Convergence Rates for Iterative Bregman Projections (Feb 1, 2026)
  66. Trajectory-Wise Certification for Vector-Field Mirror Descent with Deterministic Finite Differences (Jan 31, 2026)
  67. Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof (Oct 27, 2025)

AI-Assisted Works on Lower Bounds and Counterexamples

  1. BFGS can converge to non-Clarke-stationary points with positive probability (Oct 25, 2026)
  2. A Convex Feasibility Problem for Which Douglas-Rachford Converges Only Weakly (Oct 20, 2026)
  3. Tight lower bounds for Lipschitz geodesically convex optimization on hyperbolic space (Oct 19, 2026)
  4. Non-Acceleration of the Heavy-Ball Method in 1D (Oct 18, 2026)
  5. Strong NP-Hardness of Rank-2 Nonnegative Matrix Factorization (Oct 15, 2026)
  6. On the Complexity of Finding Stationary Points in Stochastic $(L_0, L_1)$-Smooth Nonconvex Optimization (Oct 15, 2026)
  7. Descending Everest with First-Order Oracles: Oracle Complexity of Convex Optimization under $(L_0,L_1)$-Smoothness (Oct 15, 2026)
  8. Does Policy Mirror Descent Converge in Policy with Non-Decomposable Mirror Maps? A Counterexample (Oct 14, 2026)
  9. On the Complexity of Finding Stationary Points of p-th Order Hölder Smooth Functions in One Dimension (Oct 12, 2026)
  10. Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets (Oct 9, 2026)
  11. Nonminimizing Attractors of Stochastic Subgradient Methods on Semialgebraic Functions (Oct 8, 2026)
  12. Stochastic Subgradient Descent at Sharply Repulsive Points: A Bounded Noise Counterexample and Gaussian Noise Avoidance (Oct 6, 2026)
  13. Near-Optimal Complexity of Finite-Sum Nonconvex-Strongly-Concave Minimax Optimization (Oct 4, 2026)
  14. Exact counterexamples to R-superlinear convergence of cyclic steepest descent (Oct 1, 2026)
  15. Asymptotic Lower Bounds for Continuous Optimization (Sep 28, 2026)
  16. No Universal Remainder Rate for Chambolle-Dossal Acceleration (Sep 25, 2026)
  17. Silver Rate Is (Almost) Optimal for Gradient Descent: The Strongly Convex Case (Sep 22, 2026)
  18. An $Ω(κ_y^8ε^{-6})$ Lower Bound for Stochastic NC-SC Bilevel Optimization with First-order Oracles (Sep 18, 2026)
  19. Bounds on the Semidefinite Programming Complexity of the Euclidean Ball (Sep 17, 2026)
  20. The Complexity of Finding Stationary Points in Nonsmooth Nonconvex Optimization (Sep 15, 2026)
  21. Optimal Deterministic First-Order Oracle Complexity for Nonconvex-Concave Minimax Optimization (Sep 13, 2026)
  22. Lower Bounds for Nonconvex-Concave Minimax Optimization (Sep 13, 2026)
  23. A Two-Dimensional Extremizer for Relatively Inexact Gradient Descent (Sep 11, 2026)
  24. Sharpness and Rigidity of the Two-Factor Recht-Re Lower Bound (Sep 11, 2026)
  25. A Simple Complexity Lower Bound for Solving $Ax=b$ (Sep 9, 2026)
  26. Silver Rate Is (Almost) Optimal for Gradient Descent (Sep 8, 2026)
  27. Stronger Lower Bounds for (Non-)Anytime Acceleration of Gradient Descent (Sep 3, 2026)
  28. Improved Gradient Descent Lower Bounds Beyond Nesterov (Sep 2, 2026)
  29. A Mini-Batch Counterexample to Last-Iterate Convergence in Definable Optimization (Aug 19, 2026)
  30. ADMM Fails to Achieve an $O(K^{-1})$ Ergodic KKT Residual Bound (Aug 17, 2026)
  31. AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block (Aug 14, 2026)
  32. A lower bound for stepsize-based acceleration of gradient descent (Aug 11, 2026)
  33. A Tight Lower Bound for Smooth Nonconvex Stochastic Optimization with Bounded Gradient Noise (Aug 10, 2026)
  34. The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity (Aug 7, 2026)
  35. On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations (Aug 5, 2026)
  36. A Counterexample to Fourier Alignment in Single-Neuron Modular Addition (Aug 5, 2026)
  37. Optimal Deterministic Oracle Complexity for Weakly Convex Optimization (Aug 4, 2026)
  38. Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$ (Jul 23, 2026)
  39. Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values (Jul 14, 2026)
  40. A Resolution of the SS--RS--GD Inequalities (Jun 16, 2026)
  41. Cesàro means of firmly nonexpansive iterates need not converge strongly (May 25, 2026)
  42. Curvature-Dependent Lower Bounds for Frank-Wolfe (May 11, 2026)
  43. Complexity of Classical Acceleration for $\ell_1$-Regularized PageRank (Feb 24, 2026)