Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים

תקציר

Motivated by a recent framework for proving global convergence to critical points of nested alternating minimization algorithms, which was proposed for the case of smooth subproblems, we first show here that non-smooth subproblems can also be handled within this framework. Specifically, we present a novel analysis of an optimization scheme that utilizes the FISTA method as a nested algorithm. We establish the global convergence of this nested scheme to critical points of non-convex and non-smooth optimization problems. In addition, we propose a hybrid framework that allows to implement FISTA when applicable, while still maintaining the global convergence result. The power of nested algorithms using FISTA in the non-convex and non-smooth setting is illustrated with some numerical experiments that show their superiority over existing methods.

שפה מקוריתאנגלית
עמודים (מ-עד)1130-1157
מספר עמודים28
כתב עתJournal of Optimization Theory and Applications
כרך199
מספר גיליון3
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - דצמ׳ 2023

ASJC Scopus subject areas

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