A semi-Bregman proximal alternating method for a class of nonconvex problems: local and global convergence analysis

Eyal Cohen (), D. Russell Luke (), Titus Pinta (), Shoham Sabach () and Marc Teboulle ()
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Eyal Cohen: Tel-Aviv University
D. Russell Luke: Universität Göttingen
Titus Pinta: Universität Göttingen
Shoham Sabach: Faculty of Data and Decision Sciences, Technion—Israel Institute of Technology
Marc Teboulle: Tel-Aviv University

Journal of Global Optimization, 2024, vol. 89, issue 1, No 2, 33-55

Abstract: Abstract We focus on nonconvex and non-smooth block optimization problems, where the smooth coupling part of the objective does not satisfy a global/partial Lipschitz gradient continuity assumption. A general alternating minimization algorithm is proposed that combines two proximal-based steps, one classical and another with respect to the Bregman divergence. Combining different analytical techniques, we provide a complete analysis of the behavior—from global to local—of the algorithm, and show when the iterates converge globally to critical points with a locally linear rate for sufficiently regular (though not necessarily convex) objectives. Numerical experiments illustrate the theoretical findings.

Keywords: Nonconvex and non-smooth minimization; Alternating minimization; Quadratic optimization; Bregman proximal splitting; Primary 49J52; 49M20; 90C26; Secondary 47H09; 65K05; 65K10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01334-4

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