HIGHER ORDER NECESSARY EFFICIENCY CONDITIONS FOR LOCAL WEAK AND HENIG EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS WITH CONSTRAINTS USING STUDNIARSKI’S DERIVATIVES

Abstract

The vector quilibrium problem with equilibrium constraints (it also called complementarity constraints) including vector variational inequalities and vector optimization problems with equilibrium constraints as special cases. The constraint qualification and optimality condition for optimization problems with equilibrium constraints are investigated by a lot of authors. Finding the suitable contraint qualifications to derive the Kuhn-Tucker conditions for optimization problems with equilibrium constraints have been extensively studied in recent years by many authors. In this article we study and develop the efficiency conditions for local weak efficient solution and local Henig efficient solution of vectơ equilibrium problems with constraints involving set and cone in Banach spaces in terms of higher order Studniaski’ derivatives.
The result obtained is applied for local superefficient solution of the problem under the suitable assumptions on the base of cone.