Relaxed Two-Step Inertial Tseng’s Extragradient Method for Nonmonotone Variational Inequalities

This work introduces a novel inertial projection method for solving the variational inequality (VI) without imposing the restrictive assumption of monotonicity on the cost operator. We establish global convergence of the proposed method under the condition that the solution set of the associated Min...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 205; no. 1; p. 7
Main Authors: Viet Thong, Duong, Ky Anh, Pham, Tien Dung, Vu
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2025
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Equilibrium flow
Inequalities
Infrastructure
Mathematical programming
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Theory of Computation
Weak convergence
47H10
65K15
47J20
Variational inequality
68W10
Two step inertial technique
47H09
Nonmonotone mapping
47J25
65Y05
Tseng’s extragradient method
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This work introduces a novel inertial projection method for solving the variational inequality (VI) without imposing the restrictive assumption of monotonicity on the cost operator. We establish global convergence of the proposed method under the condition that the solution set of the associated Minty VI with it is non-empty. Our results improve upon and extend many important related results in this research direction, providing a more general and flexible framework for tackling non-monotone variational inequalities. To demonstrate the practical efficacy of our method, we give some numerical illustrations and apply the proposed algorithm to solve a network equilibrium flow problem, which is a fundamental problem in transportation infrastructure modeling. We also compare the performance of our algorithm with those of existing ones.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02622-7