Single projection method for pseudo-monotone variational inequality in Hilbert spaces. (2nd January 2019)

• Record Type: Journal Article
• Authors: Shehu, Yekini; Dong, Qiao-Li; Jiang, Dan
• Is Part Of: Optimization. Volume 68:Number 1(2019)
• Page Start: 385
• Page End: 409
• Publication Date: 2019-01-02
• Subjects: Variational inequality -- pseudo-monotone mapping -- projection method -- strong convergence -- Hilbert spaces; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1522636
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, a projection-type approximation method is introduced for solving a variational inequality problem. The proposed method involves only one projection per iteration and the underline operator is pseudo-monotone and L -Lipschitz-continuous. The strong convergence result of the iterative sequence generated by the proposed method is established, under mild conditions, in real Hilbert spaces. Sound computational experiments comparing our newly proposed method with the existing state of the art on multiple realistic test problems are given.