ON NECESSARY OPTIMALITY CONDITIONS FOR LOCAL WEAK PARETO MINIMUM IN VECTOR OPTIMIZATION PROBLEM WITH CONSTRAINTS

Abstract

The vector optimization problem with set and inequalities constraints (also called as multiobjective optimization problem with constraints) is considered in this paper for which the data is of real Banach spaces. Using the regularity condition in the sense of Clarke’s derivatives in which the objective function and the constraints function are Gâteaux differentiable at the given optimal point, we provide the dual second-order nec- essary optimality condition for the local weak Pareto minimum of the vector optimization problem through the Clarke generalized derivatives and the Páles-Zeidan type second- order upper generalized directional derivatives. The result obtained in the literature is new and also illustrated by an example for our findings.