On Vector Equilibrium Problems and Applications

Abstract

The main purpose of this paper is the study of sufficient conditions for the existence of solutions of vector equilibrium problems. Our main results permit to obtain some existence results already established for the scalar case and, to provide some applications in the area of vector optimization and vector saddle point problems.

Sensitivity analysis of the solution map of parametric operator equilibrium problems

“…The equilibrium theory provides a unified, natural, innovative and general framework for the study of a large variety of problems such as optimization problems, fixed points problems, variational inequalities, Nash equilibria, saddle point problems and complementarity problems as special cases (see [3], [6], [15]). The problems mentioned above often occur in mechanics, physics, finance, economics, network analysis, transportation and elasticity.…”

Existence Theorems for Vector Equilibrium Problems via Quasi‐Relative Interior

“…The interest of the researchers on this topic is due to the fact that equilibrium problems represent a natural and unified framework for other problems, such as optimization problems, variational inequality problems, and saddle-point problems, problems which until now were separately studied and have applications in physics, economics, and so forth, (see, for instance, [2]). Since then, a large variety of vector equilibrium problems were considered and the authors studied the existence of solutions (see, for instance, [3–10]), well posedness (see, for instance, [11, 12]), and sensitivity analysis (see, for instance, [13, 14]).…”