Modified Popov's explicit iterative algorithms for solving pseudomonotone equilibrium problems
Habib ur Rehman, Poom Kumam, Yeol Je Cho, Yusuf I. Suleiman, Wiyada Kumam
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.