math.OC · 2026-09-20 · No. 119

Optimization and Control, 2026-09-20.

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

01 — The papers

3 entries
  1. 01

    Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates

    David Martínez-Rubio, Cristóbal Guzmán

    math.OC · cs.LG

    We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$-Lipschitz convex functions with respect to the $\ell_{q}$-norm over an $\ell_{p}$-ball of radius $R$, where $1\leq p,q\leq \infty$. For $p<q$, we obtain error $\widetilde{O}_{p,q}(GR/T^{1/p-(1/q-1/2)_{+}})$ after $T$ oracle queries, efficiently realizing the nearly optimal rates of (MBG+26), thereby resolving the nonsmooth end of the COLT 2015...

    arxiv.org/abs/2609.20701 · PDF

  2. 02

    The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings

    David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán, Mathieu Molina

    math.OC · cs.LG

    We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors. Our rates include \(\widetilde O(1/T)\) for convex...

    arxiv.org/abs/2609.20687 · PDF

  3. 03

    Near-Optimal Pure Single-Loop Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization

    Minhao Zhang, Zi Xu

    math.OC · cs.LG · stat.ML

    We study smooth strongly convex--strongly concave minimax optimization with general nonlinear coupling in the deterministic unconstrained setting. We propose a pure single-loop damped extragradient method with fixed parameters and two new full-gradient evaluations per iteration after one initialization query. The method uses an auxiliary feedback recursion and requires no inner solves, accuracy schedules, or staged restarts. We establish...

    arxiv.org/abs/2609.20327 · PDF

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