New inertial forward-backward type for variational inequalities with Quasi-monotonicity

Chinedu Izuchukwu (), Yekini Shehu () and Jen-Chih Yao ()
Additional contact information
Chinedu Izuchukwu: The Technion–Israel Institute of Technology
Yekini Shehu: Zhejiang Normal University
Jen-Chih Yao: China Medical University

Journal of Global Optimization, 2022, vol. 84, issue 2, No 8, 464 pages

Abstract: Abstract In this paper, we present a modification of the forward-backward splitting method with inertial extrapolation step and self-adaptive step sizes to solve variational inequalities in a quasi-monotone setting. Our proposed method involves one computation of the projection onto the feasible set and one evaluation of the operator per iteration, which is simpler than most methods available in the literature to solve similar problems. We first establish weak convergence result when the set of solutions of the Minty formulation of the variational inequality is nonempty in infinite dimensional Hilbert spaces under appropriate conditions. Next, we give linear convergence result when the operator is strongly pseudo-monotone. We also give numerical implementations of our proposed method and some comparisons with some other methods available in the literature.

Keywords: Variational inequalities; Quasi-monotone; Inertial projection method; Weak convergence; Linear convergence; Hilbert spaces; 47H05; 47J20; 47J25; 65K15; 90C25 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-022-01152-0 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:jglopt:v:84:y:2022:i:2:d:10.1007_s10898-022-01152-0

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-022-01152-0

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

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