math.OC · 2026-07-23 · No. 62

Optimization and Control, 2026-07-23.

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

    Lipschitzian SLLNs for random functions

    Lai Tian, Johannes O. Royset

    math.OC · cs.LG · math.ST

    We prove strong laws of large numbers for locally Lipschitz functions in the Lipschitz pseudometric. Our results hold under either a topological or a model-theoretic condition, with the latter encompassing functions jointly definable in o-minimal structures but extending substantially beyond this class. Applications include uniform convergence of limiting and Clarke subdifferentials and finite-sample identification of solutions. Consequently,...

    arxiv.org/abs/2607.20411 · PDF

  2. 02

    Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions

    Zhanyuan Cai, Emre Sahinoglu, Shahin Shahrampour

    math.OC · cs.LG · cs.MA

    We study decentralized online optimization for strongly geodesically convex (strongly g-convex) losses on Riemannian manifolds with bounded sectional curvature, including positively curved manifolds. In centralized Riemannian optimization, strong g-convexity tightens the optimal regret from $O(\sqrt{T})$ to $O(\log T)$, where $T$ is the time horizon; in the decentralized Riemannian setting, however, existing methods address only g-convex...

    arxiv.org/abs/2607.20316 · PDF

  3. 03

    Online Optimization of Difference-of-Convex Compositions with Smooth Mappings

    Jingwei Ji, Jong-Shi Pang, Renyuan Xu

    math.OC · cs.LG

    We study online optimization for a broad class of structured non-convex non-smooth problems where each loss is a composition of a difference-of-convex function with a smooth mapping, and the feasible region is defined by constraint functions of the same kind. We propose a time-smoothed proximal linear algorithm and a local-regret measure based on a proximal residual mapping. We show that this residual is a proper stationarity measure for the...

    arxiv.org/abs/2607.19553 · PDF

  4. 04

    Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent States

    Faraz Dadgostari, Neda Nazemi

    math.OC · cs.LG · eess.SY

    Power grids, markets, and interacting populations, settle into feedback driven equilibria observed through unknown sensors. Our Equilibrium Causal Game (ECG) joins a game to its cyclic causal model, hidden inputs, sensor map, and rules for interventions and equilibrium selection; interventions edit declared objects and recompute equilibrium. Under stated conditions, ECG-separation is sound but incomplete in our examples. Back-door/half-trek...

    arxiv.org/abs/2607.19531 · PDF

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