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*, Marc Teboulle

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalJournal of Global Optimization
DOIs
StateAccepted/In press - 2023

Keywords

  • Alternating minimization
  • Bregman proximal splitting
  • Nonconvex and non-smooth minimization
  • Quadratic optimization

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