An Explicit Extragradient Algorithm for Solving Variational Inequalities

Dang Van Hieu (), Jean Jacques Strodiot () and Le Dung Muu ()
Additional contact information
Dang Van Hieu: Ton Duc Thang University
Jean Jacques Strodiot: University of Namur
Le Dung Muu: TIMAS, Thang Long University

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 9, 476-503

Abstract: Abstract In this paper, we introduce an explicit iterative algorithm for solving a (pseudo) monotone variational inequality under Lipschitz condition in a Hilbert space. The algorithm is constructed around some projections incorporated by inertial terms. It uses variable stepsizes which are generated at each iteration by some simple computations. Furthermore, it can be easily implemented without the prior knowledge of the Lipschitz constant of the operator. Theorems of weak convergence are established under mild conditions, and some numerical results are reported for the purpose of comparison with other algorithms. The obtained results in this paper extend some related works in the literature.

Keywords: Variational inequality; Projection method; Inertial method; 65Y05; 65K15 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-020-01661-6 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:185:y:2020:i:2:d:10.1007_s10957-020-01661-6

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

DOI: 10.1007/s10957-020-01661-6

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 ().