math.OC · 2026-09-09 · No. 110

Optimization and Control, 2026-09-09.

4 new papers in math.OC. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

4 entries
  1. 01

    Silver Rate Is (Almost) Optimal for Gradient Descent Acceleration

    Yuhan Ye, Kaizhao Liu

    math.OC · cs.LG

    We study how far gradient descent (GD) can be accelerated by predetermined nonnegative stepsizes in smooth convex optimization. Writing $p_{\mathrm{sil}}=\log_2(1+\sqrt{2})$, we prove an $Ω\left(n^{-p_{\mathrm{sil}}-O(\sqrt{\log\log n/\log n})}\right)$ non-anytime lower bound. In the anytime setting, every infinite nonnegative schedule has infinitely many horizons with error...

    arxiv.org/abs/2609.09152 · PDF

  2. 02

    Distributed Linear Programming on GPU Clusters at Extreme Scale

    Arnaud Deza, Santanu Dey, Pascal Van Hentenryck

    math.OC · cs.DC

    Large linear programs can exceed the memory of a single compute node. Although first-order methods replace sparse factorizations with GPU-suited matrix-vector products, other solver phases can reintroduce a single-node memory limit. We present SHARDLP, a distributed GPU LP solver that keeps the matrix and primal-dual state partitioned from sharded input through solution output. On the Google PDLP benchmark, SHARDLP reaches the published...

    arxiv.org/abs/2609.09108 · PDF

  3. 03

    The Exact Time-Uniform Rate Frontier for Stochastic Gradient Descent on Smooth Convex Objectives

    Ruijie Li, Kang Chen, Tianyu Wang

    math.OC · cs.LG · stat.ML

    We study the time-uniform convergence of the raw iterate of standard stochastic gradient descent (SGD) for unconstrained smooth convex objectives. We prove that, under standard noise assumptions, the time-uniform convergence rate gets arbitrarily close to $\sqrt{\log n / n}$ but never reaches it. More specifically, we prove that for every positive, eventually nondecreasing sequence $h$ satisfying $h(n) = o(\sqrt{n})$, a bound of order...

    arxiv.org/abs/2609.08537 · PDF

  4. 04

    How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyond

    Ahmet Alacaoglu

    math.OC · cs.LG

    We study the stochastic first-order oracle complexity for constrained or regularized convex-concave min-max optimization and stochastic monotone variational inequalities. We focus on the case when suboptimality is measured in terms of the gradient mapping, also known as, forward-backward or natural residual, an optimality notion that generalizes the gradient norm for unconstrained problems. In this setting, under standard unbiased oracle...

    arxiv.org/abs/2609.08380 · PDF

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