Convergence Rates for the Alternating Minimization Algorithm in Structured Nonsmooth and Nonconvex Optimization
Optimization and Control
2026-02-02 v1
Abstract
This paper is devoted to developing the alternating minimization algorithm for problems of structured nonconvex optimization proposed by Attouch, Bolt\'e, Redont, and Soubeyran in 2010. Our main result provides significant improvements of the convergence rate of the algorithm, especially under the low exponent Polyak-{\L}ojasiewicz-Kurdyka condition when we establish either finite termination of this algorithm or its superlinear convergence rate instead of the previously known linear convergence. We also investigate the PLK exponent calculus and discuss applications to noncooperative games and behavioral science.
Cite
@article{arxiv.2601.22850,
title = {Convergence Rates for the Alternating Minimization Algorithm in Structured Nonsmooth and Nonconvex Optimization},
author = {Glaydston C. Bento and Boris S. Mordukhovich and Tiago S. Mota and Antoine Soubeyran},
journal= {arXiv preprint arXiv:2601.22850},
year = {2026}
}
Comments
19 pages