On Approximating Solutions to Non-monotone Variational Inequality Problems: An Approach Through the Modified Projection and Contraction Method

Duong Viet Thong (), Vu Tien Dung (), Pham Thi Huong Huyen () and Hoang Thi Thanh Tam ()
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Duong Viet Thong: National Economics University
Vu Tien Dung: Department of Mathematics, Vietnam National University
Pham Thi Huong Huyen: National Economics University
Hoang Thi Thanh Tam: National Economics University

Networks and Spatial Economics, 2024, vol. 24, issue 4, No 2, 789-818

Abstract: Abstract In this paper, we introduce a novel approach to approximate the solution of variational inequality problems without relying on the monotonicity assumption. We propose a two-step inertial modified projection and contraction method for solving quasi-monotone and without-monotone variational inequalities in real Hilbert spaces. We establish a weak convergence result for the proposed method under suitable conditions. Additionally, numerical examples and a network equilibrium flow problem are provided to illustrate the effectiveness of our method and compare it with recent related methods in the literature.

Keywords: Modified projection and contraction method; Two-step inertial; Variational inequality problem; Non-monotone mapping; Weak convergence.; 47H09; 47H10; 47J20; 47J25; 65Y05; 65K15; 68W10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11067-024-09638-y

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