Two-step inertial Bregman alternating minimization algorithm for nonconvex and nonsmooth problems

In this paper, we propose an algorithm combining Bregman alternating minimization algorithm with two-step inertial force for solving a minimization problem composed of two nonsmooth functions with a smooth one in the absence of convexity. For solving nonconvex and nonsmooth problems, we give an abst...

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Bibliographic Details
Published in:Journal of global optimization Vol. 84; no. 4; pp. 941 - 966
Main Authors: Zhao, Jing, Dong, Qiao-Li, Rassias, Michael Th, Wang, Fenghui
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Convergence
Convexity
Decomposition
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Partial differential equations
Real Functions
Regularization
Theorems
Nonconvex optimization
90C30
49J52
Alternating minimization
65K10
90C26
47J06
Bregman distance
Inertial algorithm
Kurdyka–Łojasiewicz inequality
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we propose an algorithm combining Bregman alternating minimization algorithm with two-step inertial force for solving a minimization problem composed of two nonsmooth functions with a smooth one in the absence of convexity. For solving nonconvex and nonsmooth problems, we give an abstract convergence theorem for general descent methods satisfying a sufficient decrease assumption, and allowing a relative error tolerance. Our result holds under the assumption that the objective function satisfies the Kurdyka–Łojasiewicz inequality. The proposed algorithm is shown to satisfy the requirements of our abstract convergence theorem. The convergence is obtained provided an appropriate regularization of the objective function satisfies the Kurdyka–Łojasiewicz inequality. Finally, numerical results are reported to show the effectiveness of the proposed algorithm.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01176-6