A new Popov's subgradient extragradient method for two classes of equilibrium programming in a real Hilbert space

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...

Full description

Saved in:
Bibliographic Details
Published in:Optimization 2021-12, Vol.70 (12), p.2675-2710
Main Authors: Rehman, Habib ur, Kumam, Poom, Dong, Qiao-Li, Peng, Yu, Deebani, Wejdan
Format: Article
Language:English
Subjects:
Convergence
Equilibrium problem
Half spaces
Hilbert space
Iterative methods
Lipschitz-type conditions
Optimization
pseudomonotone bifunction
strongly pseudomonotone bifunction
Theorems
variational inequality problems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1797026