Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2510.03187

ProxSTORM -- A Stochastic Trust-Region Algorithm for Nonsmooth Optimization

Robert J. Baraldi·Aurya Javeed·Drew P. Kouri·Katya Scheinberg
View original source ↗Read source document ↗Export metadata ↓

Abstract

We develop a stochastic trust-region algorithm for minimizing the sum of a Lipschitz-smooth but possibly nonconvex function and a convex but possibly nonsmooth function. Such a problem class arises in many applications, including data science, operations research, and PDE-constrained optimization. This algorithm, which we call ProxSTORM, generalizes STORM [15,11]-a stochastic trust-region algorithm for the unconstrained optimization of smooth functions-and the inexact deterministic proximal trust-region algorithm in [5]. In the absence of a nonsmooth term, we recover the original STORM algorithm, moreover, we improve and simplify certain aspects of STORM analysis, while maintaining STORM martingale framework arguments to prove global convergence and an expected complexity bound. We demonstrate ProxSTORM capabilities on neural network training and topology optimization under uncertainty.

Explore related subjects

math.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Robert J. Baraldi, Aurya Javeed, Drew P. Kouri, Katya Scheinberg. 2026-06-26. ProxSTORM -- A Stochastic Trust-Region Algorithm for Nonsmooth Optimization. https://arxiv.org/abs/2510.03187

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Riemannian Convex Bundle Method

We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds of bounded sectional curvature. Each step of our method is based on a model that involves the convex hull of previously collected subgradients, parallelly transported into the current serious iterate. This approach generalizes the dual form of classical bundle subproblems in Euclidean space. We prove that, under mild conditions, the convex bundle method converges to a minimizer. Several numerical examples implemented using Manopt$.$jl illustrate the performance of the proposed method and compare it to the subgradient method, the cyclic proximal point algorithm, as well as the proximal bundle method.

math.OC↗
arXiv2026

Omega-Limit Sets and Input-to-State Stability in Power Grids With Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields -- or modes--, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of $Ω$-limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

math.OC↗
arXiv2026

Cellular flow control design for mixing based on the least action principle

We consider a novel approach for the enhancement of fluid mixing via pure stirring strategies building upon the Least Action Principle (LAP) for incompressible flows. The LAP is formally analogous to the Benamou--Brenier formulation of optimal transport, but imposes an incompressibility constraint. Our objective is to find a velocity field, generated by Hamiltonian flows, that minimizes the kinetic energy while ensuring that the initial scalar distribution reaches a prescribed degree of mixedness by a finite time. This formulation leads to a ``point-to-set" type of optimization problem which relaxes the requirement on controllability of the system compared to the classic LAP framework. In particular, we assume that the velocity field is induced by a finite set of cellular flows that can be controlled in time. To establish finite time feasibility, we introduce an operator-theoretic switching argument that combines the long-time cellular flow mixing result with the von Neumann alternating-projection theorem. We then leverage the direct method to establish the existence of an optimal solution. Finally, we derive the corresponding optimality conditions for the time-dependent control problem and conduct numerical experiments demonstrating the effectiveness of the proposed control design.

math.OC↗