A Bregman inertial forward-reflected-backward method for nonconvex minimization

We propose a Bregman inertial forward-reflected-backward (BiFRB) method for nonconvex composite problems. Assuming the generalized concave Kurdyka-Łojasiewicz property, we obtain sequential convergence of BiFRB, as well as convergence rates on both the function value and actual sequence. One disting...

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Bibliographic Details
Published in:Journal of global optimization Vol. 89; no. 2; pp. 327 - 354
Main Authors: Wang, Xianfu, Wang, Ziyuan
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2024
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Computer Science
Convergence
Euclidean space
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Operations Research/Decision Theory
Optimization
Parameters
Real Functions
Nonconvex optimization
49J52
Secondary 26D10
Generalized concave Kurdyka-Łojasiewicz property
Forward-reflected-backward splitting
Bregman proximal mapping
Inertial effect
Primary 90C26
Implicit merit function
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We propose a Bregman inertial forward-reflected-backward (BiFRB) method for nonconvex composite problems. Assuming the generalized concave Kurdyka-Łojasiewicz property, we obtain sequential convergence of BiFRB, as well as convergence rates on both the function value and actual sequence. One distinguishing feature in our analysis is that we utilize a careful treatment of merit function parameters, circumventing the usual restrictive assumption on the inertial parameters. We also present formulae for the Bregman subproblem, supplementing not only BiFRB but also the work of Boţ-Csetnek-László and Boţ-Csetnek. Numerical simulations are conducted to evaluate the performance of our proposed algorithm.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-023-01348-y