math.OC · 2026-07-09 · No. 48

Optimization and Control, 2026-07-09.

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

    POO-LPSP: Parallel Osprey Optimized Least Penalty-Squared Prioritization Methods for Priority Derivation in the Analytic Hierarchy Process

    Kevin Kam Fung Yuen

    math.OC · cs.AI · cs.DC · math.NA

    Pairwise comparison (PC) via pairwise reciprocal matrices (PRMs) is central to the Analytic Hierarchy Process (AHP). Although the traditional eigenvector method is widely applied to derive priorities, its theoretical robustness in reflecting true priority vectors remains debated. Building upon a previous iteration of this study, this research develops the revised Least Penalty-Squared Prioritization (LPSP) optimization models, including the...

    arxiv.org/abs/2607.07313 · PDF

  2. 02

    Restricted Dynamic Geometric Complexity: Certificates for Structured Preconditioning

    Zavier Li

    math.OC · cs.LG

    Optimization geometrodynamics views optimizer state as evolving geometry. Its full positive-definite quadratic benchmark gives the least affine-invariant deformation needed to reduce condition number when arbitrary metrics are allowed. This paper records that benchmark in the present notation and develops restricted dynamic geometric complexity: an intrinsic certificate distance for reaching a target condition-number class when the metric is...

    arxiv.org/abs/2607.07204 · PDF

  3. 03

    Mathematical methods of reinforcement learning

    Denis Belomestny, Alexander Gasnikov, Egor Gladin, Alexey Naumov, Artemy Rubtsov, Yuri Sapronov, Daniil Tiapkin, Nikita Yudin

    math.OC · cs.LG

    Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates for value and policy...

    arxiv.org/abs/2607.06935 · PDF

  4. 04

    Optimization Geometrodynamics: A Framework for Dynamic Geometric Optimization

    Zavier Li

    math.OC · cs.LG · math.DG

    Most gradient-based optimization methods move parameters through a fixed background geometry, even when their internal states implicitly define changing notions of length, curvature, and preconditioning. We introduce optimization geometrodynamics, a benchmark language in which optimization is a coupled evolution of a parameter trajectory, a transported distribution of particles, and a controlled time-varying Riemannian metric. The language...

    arxiv.org/abs/2607.06723 · PDF

This edition is part of The Daily Abstract — math.OC archive. Subscribe to receive these in your inbox each morning, automatically translated to Spanish, with reply-to-PDF: arxivdaily.ignorelist.com.

Colophon Set in Georgia, with system sans for interface chrome and a monospaced stack for code and paper identifiers. Sole accent: amber #D99C5E. Built and served on an always-free VM. The masthead is set 14% letterspaced because newspapers do that and it works.