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

Duong Viet Thong (), Vu Tien Dung () and Hoang Thi Thanh Tam ()
Additional contact information
Duong Viet Thong: National Economics University
Vu Tien Dung: Vietnam National University
Hoang Thi Thanh Tam: National Economics University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 17, 27 pages

Abstract: Abstract 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.

Keywords: Variational inequalities; Non-monotone mapping; Weak convergence; Linear convergence rate; 47H09; 47H10; 47J20; 47J25; 65Y05; 65K15; 68W10 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02674-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:206:y:2025:i:1:d:10.1007_s10957-025-02674-9

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02674-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().