RT Journal Article
SR 00
ID 10.1007/s10107-013-0701-9
A1 Bolte, Jérôme
A1 Sabach, Shoham
A1 Teboulle, Marc
T1 Proximal alternating linearized method for nonconvex and nonsmooth problems
JF Mathematical Programming
YR 2014
FD 2014-08
VO 146
SP 459
OP 494
AB 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 sequence generated by PALM globally converges to a critical point. Our approach allows to analyze various classes of nonconvex-nonsmooth problems and related nonconvex proximal forward–backward algorithms with semi-algebraic problem’s data, the later property being shared by many functions arising in a wide variety of fundamental applications. A by-product of our framework also shows that our results are new even in the convex setting. As an illustration of the results, we derive a new and simple globally convergent algorithm for solving the sparse nonnegative matrix factorization problem.
PB Springer
SN 0025-5610
LK https://publications.ut-capitole.fr/id/eprint/16696/
UL http://tse-fr.eu/pub/29008