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

Eyal Gur (), Shoham Sabach () and Shimrit Shtern ()
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Eyal Gur: Technion – Israel Institute of Technology
Shoham Sabach: Technion – Israel Institute of Technology
Shimrit Shtern: Technion – Israel Institute of Technology

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 3, No 11, 1130-1157

Abstract: Abstract 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.

Keywords: Non-convex and non-smooth optimization; Alternating minimization; Global convergence; Nested algorithms; FISTA; 90C06; 90C26; 90C30; 90C90 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02310-4

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