Proximal alternating linearized minimization for nonconvex and nonsmooth problems

• Published in: Mathematical programming Vol. 146; no. 1-2; pp. 459 - 494
• Main Authors: Bolte, Jérôme, Sabach, Shoham, Teboulle, Marc
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Analysis; Byproducts; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Construction; Data smoothing; Full Length Paper; Functions (mathematics); Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical programming; Mathematics; Mathematics and Statistics; Mathematics of Computing; Minimization; Numerical Analysis; Optimization; Optimization and Control; Palm; Studies; Theoretical; Gauss-Seidel method; Kurdyka–Łojasiewicz property; Block coordinate descent; Alternating minimization; 90C26; Nonconvex-nonsmooth minimization; Proximal forward-backward; 90C30; 65K10; 49M27; 49M37; 47J25; Sparse nonnegative matrix factorization

We introduce a proximal alternating linearized minimization (PALM) algorithm for solving a broad class of nonconvex and nonsmooth minimization problems. Building on the powerful Kurdyka–Łojasiewicz property, we derive a self-contained convergence analysis framework and establish that each bounded se...