Splitting Proximal Point Algorithms for the Sum of Prox-Convex Functions
Optimization and Control
2026-01-13 v1
Abstract
This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one deterministic with a fixed update order, and one stochastic with random sampling, and we extend them from convex to prox-convex functions. We prove global convergence for both methods under standard stepsize a\-ssump\-tions, with almost sure convergence for the stochastic variant via supermartingale theory. Numerical experiments with nonconvex quadratic functions illustrate the efficiency of the proposed methods and support the theoretical results.
Cite
@article{arxiv.2601.06970,
title = {Splitting Proximal Point Algorithms for the Sum of Prox-Convex Functions},
author = {Jose de Brito and Felipe Lara and Tran Van Thang},
journal= {arXiv preprint arXiv:2601.06970},
year = {2026}
}