A Self Adaptive Projected Gradient Method for Solving Non-Monotone Variational Inequalities

被引：0

作者：

Duong Viet Thong ^{[1
]}

Vu Tien Dung ^{[2
]}

Hoang Thi Thanh Tam ^{[3
]}

机构：

[1] National Economics University,Fundamental Sciences Faculty

[2] Vietnam National University,Department of Mathematics

[3] National Economics University,Faculty of Mathematical Economics

来源：

Journal of Optimization Theory and Applications | 2025年 / 206卷 / 1期

关键词：

Variational inequalities; Non-monotone mapping; Weak convergence; Linear convergence rate; 47H09; 47H10; 47J20; 47J25; 65Y05; 65K15; 68W10;

D O I：

10.1007/s10957-025-02674-9

中图分类号：

学科分类号：

摘要：

In this paper, we introduce a new modified golden ratio algorithm with adaptive stepsize rules for solving non-monotone variational inequalities in infinite-dimensional Hilbert spaces. The weak convergence and convergence rate of the proposed algorithm are established under some standard conditions. Finally, to demonstrate the practical efficacy of our method, we give some numerical illustrations and we apply the proposed algorithm to solve a network equilibrium flow problem, which is a fundamental problem in transportation infrastructure modeling. Additionally, we compare the performance of our algorithm with other existing methods.

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