math.OC · 2026-08-13 · No. 83

Optimization and Control, 2026-08-13.

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

    The Advective Fisher-Rao Geometry of Deterministic Measure Transport

    Benjamin Gess, Johannes Müller

    math.OC · cs.LG · math.DG · math.PR

    A novel advective Fisher-Rao metric is introduced for optimization tasks on paths of probability measures governed by the continuity equation. This metric is shown to lead to optimal descent directions. It is then shown that this metric arises naturally from three different perspectives: As the rescaled zero-noise limit of the Fisher-Rao metric on path measures, as the expected value of the second variation of the Freidlin--Wentzell large...

    arxiv.org/abs/2608.12111 · PDF

  2. 02

    Direct Acceleration of Stochastic Root-Finding Without Variance Reduction and Regularization

    TaeHo Yoon, Nicolas Loizou

    math.OC · cs.LG

    Acceleration for deterministic root-finding problems has been extensively studied in recent years; specifically, the anchor-based, or Halpern-type methods achieve optimal convergence rates with respect to the operator norm. However, acceleration via these methods does not directly carry over to stochastic setting due to accumulation of errors, unless one enforces diminishing variance via increasing batch sizes or variance reduction...

    arxiv.org/abs/2608.12043 · PDF

  3. 03

    Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size

    Chenhan Jin, Shengze Xu, Binghui Xie, Kaiwen Zhou, Fan Jia, James Cheng, Tieyong Zeng

    math.OC · cs.LG

    Bregman proximal stochastic gradient (BPSG) methods bring variance-reduced composite optimization to objectives whose geometry is poorly captured by Euclidean smoothness. Their performance, however, remains sensitive to the step size: raw stochastic curvature estimates can fluctuate sharply, whereas line searches add repeated proximal evaluations. We introduce Ada-BPSG, a line-search-free BPSG method that couples the SAGA gradient table with...

    arxiv.org/abs/2608.12009 · PDF

  4. 04

    Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp

    Wenzhi Gao, Zhaonan Qu, Yinyu Ye, Madeleine Odell

    math.OC · cs.LG · stat.ML

    We revisit the Sinkhorn-Knopp (SK) algorithm for the matrix scaling problem. Despite extensive literature on the global convergence of SK and its variants, its local linear convergence behavior remains less understood. We address this gap by providing the first nonasymptotic local analysis of SK that matches the rate obtained from existing asymptotic Jacobian-based arguments. We show that under certain connectivity conditions, SK is a...

    arxiv.org/abs/2608.11760 · PDF

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