Convergent Nested Alternating Minimization Algorithms for Nonconvex Optimization Problems

Eyal Gur (), Shoham Sabach () and Shimrit Shtern ()
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Eyal Gur: Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 3200003, Israel
Shoham Sabach: Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 3200003, Israel
Shimrit Shtern: Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 3200003, Israel

Mathematics of Operations Research, 2023, vol. 48, issue 1, 53-77

Abstract: We introduce a new algorithmic framework for solving nonconvex optimization problems, that is called nested alternating minimization , which aims at combining the classical alternating minimization technique with inner iterations of any optimization method. We provide a global convergence analysis of the new algorithmic framework to critical points of the problem at hand, which to the best of our knowledge, is the first of this kind for nested methods in the nonconvex setting. Central to our global convergence analysis is a new extension of classical proof techniques in the nonconvex setting that allows for errors in the conditions. The power of our framework is illustrated with some numerical experiments that show the superiority of this algorithmic framework over existing methods.

Keywords: Primary: 90C26; 90C30; 49M37; 65K10; nonconvex and nonsmooth minimization; nested algorithms; nondescent methods; nonsmooth Kurdyka-Łojasiewicz property; global convergence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:1:p:53-77

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