LAGRANGE MULTIPLIERS IN MULTIOBJECTIVE OPTIMIZATION UNDER MIXED ASSUMPTIONS OF FRECHET AND DIRECTIONAL DIFFERENTIABILITY

Abstract

We study a multiobjective optimization problem in finite-dimensional spaces with a feasible set defined by directionally differentiable (or quasiconvex) inequality constraints and Fréchet differentiable equality constraints. Under a suitable constraint qualification (of the Mangasarian-Fromovitz type) an expression for the contingent cone to the feasible set is obtained. As application, necessary conditions of Pareto optimality both Fritz John type and Kuhn-Tucker type are obtained by means of Lagrange multipliers rules.