arXiv AI August 17, 2026 By Kenan Xu, Xiangfeng Wang

AI-Assisted Discovery and Construction of a Counterexample to the Convergence of Three-Block ADMM with the Identity Matrix as its Third Constraint Block

arXiv:2608. 14396v1 Announce Type: cross Abstract: The alternating direction method of multipliers (ADMM), as a landmark algorithm, has attracted tremendous research attention and extensive practical applications over the past two decades.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.

llms

arXiv Machine Learning

Jul 9

Geometric--Nongeometric Optimizer Calculus: A Modular Language for Reachable Gradient Methods

arXiv:2607. 07206v1 Announce Type: new Abstract: Adaptive optimizers mix several mechanisms: a metric or preconditioner maps gradients to descent directions, while estimation, memory, step-size control, constraints, stochasticity, target modification, and discretization determine which directions are available and how they are used.

By Zavier Li

benchmarks

arXiv Machine Learning

Jul 9

Restricted Dynamic Geometric Complexity: Certificates for Structured Preconditioning

arXiv:2607. 07204v1 Announce Type: cross Abstract: Optimization geometrodynamics views optimizer state as evolving geometry.

By Zavier Li

benchmarks

arXiv Machine Learning

Jul 27

Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programs

arXiv:2607. 22263v1 Announce Type: cross Abstract: A data-driven inverse optimization problem (DDIOP) is the problem of estimating the objective-function parameters (weights) that explain observed optimal-solution data, and it arises in many applications, including integer linear programming (ILP).

By Akira Kitaoka

arXiv Machine Learning

Jul 14

Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response

arXiv:2607. 07204v2 Announce Type: replace-cross Abstract: Structured preconditioners restrict optimization to a small family of positive metrics, but endpoint condition-number reachability does not measure the geometric effort required to reach a useful metric.

By Zavier Li

arXiv AI

Jun 3

Optimizing Explicit Unit-Distance Lower-Bound Certificates

arXiv:2606. 03419v1 Announce Type: cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's subsequent explicit quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$.

By Michael T. M. Emmerich

arXiv Machine Learning

Jun 2

Accelerating Min-Max Optimization via Power-Law Stepsizes

arXiv:2606. 01764v1 Announce Type: cross Abstract: We revisit the convergence guarantees of the Extragradient (EG) method for unconstrained biaffine min-max optimization.

By Yue Wu, Weiqiang Zheng, Yang Cai, Haipeng Luo

Related stories

Geometric--Nongeometric Optimizer Calculus: A Modular Language for Reachable Gradient Methods

Restricted Dynamic Geometric Complexity: Certificates for Structured Preconditioning

Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programs

Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response

Optimizing Explicit Unit-Distance Lower-Bound Certificates

Accelerating Min-Max Optimization via Power-Law Stepsizes