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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Eyal Cohen & D. Russell Luke & Titus Pinta & Shoham Sabach & Marc Teboulle, 2024. "A semi-Bregman proximal alternating method for a class of nonconvex problems: local and global convergence analysis," Journal of Global Optimization, Springer, vol. 89(1), pages 33-55, May.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:1:d:10.1007_s10898-023-01334-4
    DOI: 10.1007/s10898-023-01334-4
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    References listed on IDEAS

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    1. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization," Computational Optimization and Applications, Springer, vol. 79(3), pages 681-715, July.
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