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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Published in | Optimization methods & software Vol. 36; no. 1; pp. 82 - 113 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Abingdon
Taylor & Francis
02.01.2021
Taylor & Francis Ltd |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1055-6788 1029-4937 |
DOI: | 10.1080/10556788.2020.1734805 |