The subgradient extragradient method for pseudomonotone equilibrium problems. (2nd April 2020)

• Record Type: Journal Article
• Authors: Dadashi, Vahid; Iyiola, Olaniyi S.; Shehu, Yekini
• Is Part Of: Optimization. Volume 69:Number 4(2020)
• Page Start: 901
• Page End: 923
• Publication Date: 2020-04-02
• Subjects: Subgradient extragradient method -- pseudo-monotone equilibrium problems -- weak convergence -- Hilbert spaces; 47H06 -- 47H09 -- 47J05 -- 47J25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1625899
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, an improvement of the extragradient algorithm is considered for finding a solution of pseudo-monotone equilibrium problems in real Hilbert spaces. We replace the second minimization problem onto a closed convex set in the extragradient method, with a subgradient projection onto some constructible half-space and propose a new method of getting the step-size. A convergence theorem for the generated sequence is proved and applied for finding a solution of variational inequality problem.