Convergence Rates for the Alternating Minimization Algorithm in Structured Nonsmooth and Nonconvex Optimization

Fuente: arXiv
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Main Authors: Bento, Glaydston C., Mordukhovich, Boris S., Mota, Tiago S., Soubeyran, Antoine
Format: Preprint
Published: 2026
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_version_ 1866910006082797568
author Bento, Glaydston C.
Mordukhovich, Boris S.
Mota, Tiago S.
Soubeyran, Antoine
author_facet Bento, Glaydston C.
Mordukhovich, Boris S.
Mota, Tiago S.
Soubeyran, Antoine
contents This paper is devoted to developing the alternating minimization algorithm for problems of structured nonconvex optimization proposed by Attouch, Bolté, Redont, and Soubeyran in 2010. Our main result provides significant improvements of the convergence rate of the algorithm, especially under the low exponent Polyak-Łojasiewicz-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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_22850
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Convergence Rates for the Alternating Minimization Algorithm in Structured Nonsmooth and Nonconvex Optimization
Bento, Glaydston C.
Mordukhovich, Boris S.
Mota, Tiago S.
Soubeyran, Antoine
Optimization and Control
90C26, 49J52, 49J53, 90D10
This paper is devoted to developing the alternating minimization algorithm for problems of structured nonconvex optimization proposed by Attouch, Bolté, Redont, and Soubeyran in 2010. Our main result provides significant improvements of the convergence rate of the algorithm, especially under the low exponent Polyak-Łojasiewicz-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.
title Convergence Rates for the Alternating Minimization Algorithm in Structured Nonsmooth and Nonconvex Optimization
topic Optimization and Control
90C26, 49J52, 49J53, 90D10
url https://arxiv.org/abs/2601.22850