Hybrid proximal methods for equilibrium problems

Hybrid proximal methods for equilibrium problems

This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another alg...

Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse stronglymonotone in a Banach space under different conditions. Moreover, applications to complementarit...

Proximal methods for a class of bilevel monotone equilibrium problems

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a simple proximal method. Under mild conditions, the weak convergence of the sequences generated by the algorithm is obtained. Using this result we obtain corollaries which improve several corresponding results in this field.

Second-order Differential Proximal Methods for Equilibrium Problems

An approximate procedure for solving equilibrium problems is proposed and its convergence is established under natural conditions. The result obtained in this paper includes, as a special case, some known results in convex minimization and monotone inclusion fields.

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points