Modified Popov's explicit iterative algorithms for solving pseudomonotone equilibrium problems

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 o...

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Bibliographic Details
Published inOptimization methods & software Vol. 36; no. 1; pp. 82 - 113
Main Authors ur Rehman, Habib, Kumam, Poom, Je Cho, Yeol, Suleiman, Yusuf I., Kumam, Wiyada
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2021
Taylor & Francis Ltd
Subjects
Algorithms
Convergence
Equilibrium problem
extragradient method
Iterative algorithms
Iterative methods
Lipschitz-type conditions
Nash-Cournot equilibrium model of electricity markets
weak convergence
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Summary: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.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2020.1734805