A new Popov's subgradient extragradient method for two classes of equilibrium programming in a real Hilbert space. (2nd December 2021)

• Record Type: Journal Article
• Authors: Rehman, Habib ur; Kumam, Poom; Dong, Qiao-Li; Peng, Yu; Deebani, Wejdan
• Is Part Of: Optimization. Volume 70:Number 12(2021)
• Page Start: 2675
• Page End: 2710
• Publication Date: 2021-12-02
• Subjects: Equilibrium problem -- pseudomonotone bifunction -- strongly pseudomonotone bifunction -- Lipschitz-type conditions -- variational inequality problems; 47H06 -- 47H09 -- 47J05 -- 47J25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1797026
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we proposed two different methods for solving pseudomonotone and strongly pseudomonotone equilibrium problems. We can examine these methods as an extension and improvement of the Popov's extragradient method. We replaced the second minimization problem onto a closed convex set in the Popov's extragradient method, with a half-space minimization problem that is updated on each iteration and also formulates a useful method for determining the appropriate stepsize on each iteration. The weak convergence theorem of the first method and strong convergence theorem for the second method is well-established based on a standard assumption on a cost bifunction. We also consider various numerical examples to support our well-established convergence results, and we can see that the proposed methods depict a significant improvement in terms of the number of iterations and execution time.