math.OC · 2026-10-05 · No. 134

Optimization and Control, 2026-10-05.

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

    From Mixing to Tearing: Graph Decomposition in Decentralized Optimization via Message Passing

    Kuangyu Ding, Gesualdo Scutari

    math.OC · cs.LG

    We study the minimization of sums of smooth strongly convex functions over undirected graphs, with each function held by one agent and communication restricted to neighbors in the graph. Existing decentralized methods, whether based on gossip or on routing over spanning trees, typically use the network to mix or aggregate information to enable {\it prescribed} local optimization updates. What this communication-centered viewpoint lacks is a...

    arxiv.org/abs/2610.03709 · PDF

  2. 02

    Information Limits of Low-Rank Approximation Certification

    Kang Liu, Bohao Qu

    math.OC · cs.AI · cs.IT

    Low-rank approximation can require additional matrix--vector products to verify that its error meets a prescribed tolerance. We characterize this certification cost for both relative matrix error and mean-square output error. For a single approximation matrix candidate, we determine the exact dimension-uniform minimax query constant as the allowed failure probability vanishes. Our main result concerns reusing validation responses as the...

    arxiv.org/abs/2610.03321 · PDF

  3. 03

    Near-Optimal Convex Optimization with Lazy Second-Order Oracles

    Xinliang Zhang, Lesi Chen, Chengchang Liu, Jingzhao Zhang

    math.OC · cs.LG · stat.ML

    This paper studies the complexity of convex optimization using lazy second-order oracles (Doikov, Chayti, and Jaggi, ICML 2023), where an algorithm queries gradients every iteration and Hessians once per $m$ iterations. Under this setting, we show a lower bound of $Ω(m+ m^{1/7} ε^{-2/7})$ on the number of total iterations to find an $ε$-solution using a novel block zero-chain construction. Then we propose a novel method that achieves a new...

    arxiv.org/abs/2610.03222 · PDF

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