Iterative Schemes for Uniformly Nonconvex Equilibrium Problems

Abstract

Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular equilibrium problems are analyzed by the aux iliary principle and inertial proximal methods. The convergence analysis of the new proposed methods is considered under some mild conditions. Gap functions are constructed to suggest some descent-type scheme for uniformly regular equilibrium problems. Our results can be viewed as significant refinements and improvements of the previously known results and they continue to hold for equilibrium problems, variational inequalities and complementarity problems as well.