An outer approximation algorithm for equilibrium problems in Hilbert spaces

Abstract

We introduce an algorithm for solving nonsmooth equilibrium problems in real Hilbert spaces. At each iteration, a regularized proximal-like equilibrium problem on a suitable outer approximation of the original constraint set is considered. We prove, under standard assumptions, that the sequence generated by the algorithm converges weakly to a solution of the problem. Some numerical experience with the algorithm is reported.

A self-adaptive viscosity-type inertial extragradient algorithm for solving monotone variational inequality and paramonotone equilibrium problem 1

“…EP In 2009, many algorithms [22][23][24][25][26] has been developed for solving the . EP Santos and Scheimberg [27] proposed an inexact projection subgradient method to solve the EP involving paramonotone bifunctions in finite dimensional space. It is noted that this algorithm only needs one projection per iteration and its weak convergence was proved under mild assumptions.…”

Abstract regularized equilibria: application to Becker’s household behavior theory

“…In this section, we illustrate our method for solving some academic problems considered in Santos and Scheimberg (2011) and Santos and Souza (2020) using different kind of regularizations. The algorithms have coded in MATLAB using the subroutine "quadprog" on a notebook 8 GB Intel Core i7 Dual-Core.…”

“…), γ j = max{1, g j }, where ∂ y F k stands to the subdifferential of F k with respect the variable y; see Santos and Scheimberg (2011).…”

“…Example 7: the initial point x 0 = (1, 3, 1, 1, 2) and = 10 −3 as inSantos and Scheimberg (2011) and λ k = 0.001…”

On fixed point approach to equilibrium problem

“…After the appearance of the paper by Blum and Oettli [11], the problem (EP) has attracted much attention of many authors and a lot of algorithms have been developed for solving the problem where the bifunction f have monotonic properties. These algorithms are based upon different methods such as penalty and gap functions [7,8,9,23,24,25,29,33], regularization [3,20,28,34,35], extragradient methods [10,19,26,37,39,40,41,44,46,47,48], splitting technique [2,15,32]. A comprehensive referencelist on algorithms for the equilibrium problem can be found in the interesting monograph [6].…”