Modified Popov's explicit iterative algorithms for solving pseudomonotone equilibrium problems. (2nd January 2021)

• Record Type: Journal Article
• Authors: ur Rehman, Habib; Kumam, Poom; Je Cho, Yeol; Suleiman, Yusuf I.; Kumam, Wiyada
• Is Part Of: Optimization methods and software. Volume 36:Number 1(2021)
• Page Start: 82
• Page End: 113
• Publication Date: 2021-01-02
• Subjects: Equilibrium problem -- extragradient method -- weak convergence -- Lipschitz-type conditions -- Nash-Cournot equilibrium model of electricity markets; 65Y05 -- 65K15 -- 47H05 -- 47H10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1734805
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : This paper proposes two algorithms that are based on a subgradient and an inertial scheme with the explicit iterative method for solving pseudomonotone equilibrium problems. The weak convergence of both algorithms is well-established under standard assumptions on the cost bifunction. The advantage of these algorithms is that they did not require any line search procedure or any knowledge about bifunction Lipschitz-type constants for step-size evaluation. A practical explanation of this is that they use a sequence of step-size that are revised at each iteration based on some previous iteration. For a numerical experiment, we consider a well-known Nash-Cournot equilibrium model of electricity markets and also other test problems to assist the well-established convergence results and be able to see that our proposed algorithms have a competitive advantage over the time of execution and the number of iterations.