Extension of forward-reflected-backward method to non-convex mixed variational inequalities

This paper presents a modification of a recently studied forward-reflected-backward splitting method to solve non-convex mixed variational inequalities. We give global convergence results and nonasymptotic O (1/ k ) rate of convergence of the proposed method under some appropriate conditions and pre...

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Bibliographic Details
Published in:Journal of global optimization Vol. 86; no. 1; pp. 123 - 140
Main Authors: Izuchukwu, Chinedu, Shehu, Yekini, Okeke, Chibueze C.
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2023
Springer
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Convergence
Convex analysis
Equilibrium
Inequalities
Iterative methods
Mathematical functions
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Real Functions
68Q25
Proximal point algorithms
90C30
90C25
90C22
Forward-reflected-backward splitting
90C60
49M25
Non-convex variational inequalities
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:This paper presents a modification of a recently studied forward-reflected-backward splitting method to solve non-convex mixed variational inequalities. We give global convergence results and nonasymptotic O (1/ k ) rate of convergence of the proposed method under some appropriate conditions and present some numerical illustrations, one of which is derived from oligopolistic equilibrium problems, to show the efficiency of our proposed method.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01253-w