@article{30b624c3e5b34bd9890cc4b5f47cac10,
title = "A semi-Bregman proximal alternating method for a class of nonconvex problems: local and global convergence analysis",
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 = "49M20, 65K05, 65K10, 90C26, Alternating minimization, Bregman proximal splitting, Nonconvex and non-smooth minimization, Primary 49J52, Quadratic optimization, Secondary 47H09",
author = "Eyal Cohen and Luke, {D. Russell} and Titus Pinta and Shoham Sabach and Marc Teboulle",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.",
year = "2024",
month = may,
doi = "10.1007/s10898-023-01334-4",
language = "אנגלית",
volume = "89",
pages = "33--55",
journal = "Journal of Global Optimization",
issn = "0925-5001",
publisher = "Springer Netherlands",
number = "1",
}