Modified two-step extragradient method for solving the pseudomonotone equilibrium programming in a real Hibert space

Abstract

The purpose of this paper is to come up with an inertial extragradient method for dealing with a class of pseudomonotone equilibrium problems. This method can be a view as an extension of the paper title “A new twostep proximal algorithm of solving the problem of equilibrium programming” by Lyashko and Semenov et al. (Optimization and Its Applications in Control and Data Sciences: 315—325, 2016). The theorem of weak convergence for solutions of the pseudomonotone equilibrium problems is well-established under standard assumptions placed on cost bifunction in the structure of a real Hilbert spaces. For a numerical experiment, we take up a well-known Nash Cournot equilibrium model of electricity markets to support the well-established convergence results and be adequate to see that our proposed algorithms have a competitive superiority over the time of execution and the number of iterations.

A novel method for solving nonmonotone equilibrium problems

“…These methods often require the convexity on the second variable and the monotonicity or generalized monotonicity of the bifunction f . Up to now, several results have been achieved for this class of equilibrium problems (see papers [1,13,22,29,32] and books [2,16]). Recently, J. Strodiot et al in [28] (see also [7,9,15]) have introduced shrinking projection algorithms to solve nonmonotone equilibrium problems.…”

Inertial Iterative Self-Adaptive Step Size Extragradient-Like Method for Solving Equilibrium Problems in Real Hilbert Space with Applications

“…Many methods have been already established over the past couple of years to figure out the equilibrium problem in Hilbert spaces [5][6][7][8][9][10][11][12][13][14][15], the inertial methods [11,[16][17][18] and others in [18][19][20][21][22][23][24]. In particular, Tran et al introduced an iterative scheme in [8], in that a sequence {u n } was generated in the following way:…”