math.OC · 2026-08-12 · No. 82

Optimization and Control, 2026-08-12.

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

    Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms

    Florian Beier, Stephan Eckstein

    math.OC · cs.CG · cs.LG · math.PR

    Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like $k$-means. Such methods are strongly connected to quantization problems, which aim to approximate general probability measures with discrete ones. For example, $k$-means corresponds to quantization with respect to the Wasserstein distance. While Wasserstein quantization clusters points within a fixed space,...

    arxiv.org/abs/2608.11016 · PDF

  2. 02

    Threshold Structure of Optimal Policies in Restart POMDPs

    Konstantin Avrachenkov, Alexey Piunovskiy, Yi Zhang

    math.OC · cs.LG · math.PR

    We study a Restart POMDP (Partially Observable Markov Decision Process) on a general Borel state space, where the controller either lets the hidden state evolve unobserved or restarts the system and observes the new state. Exploiting a sufficient-statistic representation consisting of the last observed state and the elapsed time since restart, we reduce the problem to a fully observed MDP. Under a natural one-step cost deterioration...

    arxiv.org/abs/2608.10936 · PDF

  3. 03

    A lower bound for stepsize-based acceleration of gradient descent

    Jianhao Ma, Yuxin Chen

    math.OC · cs.LG · stat.ML

    Recent work has shown that, for smooth convex optimization, plain gradient descent can be accelerated from its textbook convergence rate of $O(T^{-1})$ (where $T$ denotes the number of iterations) to $O\big(T^{-\log_2(1+\sqrt{2})}\big)$ using carefully designed stepsize schedules alone, without resorting to momentum or other algorithmic modifications. Despite this progress, however, little was known about lower bounds for such methods beyond...

    arxiv.org/abs/2608.10418 · PDF

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