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

Glaydston C. Bento, Boris S. Mordukhovich, Tiago S. Mota and Antoine Soubeyran
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Glaydston C. Bento: Federal University of Goiás
Boris S. Mordukhovich: Wayne State University [Detroit]
Tiago S. Mota: Federal University of Goiás
Antoine Soubeyran: Aix Marseille Univ, CNRS, AMSE, Marseille, France

No 2609, AMSE Working Papers from Aix-Marseille School of Economics, France

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 PolyakLojasiewicz-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 behavioralscience.

Keywords: Polyak- Lojasiewicz-Kurdyka conditions; Convergence rates; Noncooperative games; Alternating minimization algorithm; Nonsmooth optimization (search for similar items in EconPapers)
Date: 2026-01-30
Note: Working paper AMSE 2026-09
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