GAP FUNCTIONS FOR NONSMOOTH EQUILIBRIUM PROBLEMS

Gap Functions for Equilibrium Problems

The theory of gap functions, developed in the literature for variational inequalities, is extended to a general equilibrium problem. Descent methods, with exact an inexact line-search rules, are proposed. It is shown that these methods are a generalization of the gap function algorithms for variational inequalities and optimization problems.

Quasi-Gap and Gap Functions for Non-Smooth Multi-Objective Semi-Infinite Optimization Problems

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

Error Bounds of Generalized D-Gap Functions for Nonsmooth and Nonmonotone Variational Inequality Problems

We present some error bound results of generalized D-gap functions for nonsmooth and nonmonotone variational inequality (VI) problems. Application is given in providing a derivative-free descent method.

Optimization Tools for Solving Equilibrium Problems with Nonsmooth Data

Benson's algorithm for nonconvex multiobjective problems via nonsmooth Wolfe duality

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also fo...