On necessary conditions for efficiency in directionally differentiable optimization problems

Abstract

This paper deals with multiobjective programming problems with inequality, equality and set constraints involving Dini or Hadamard differentiable functions. A theorem of the alternative of Tucker type is established and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Directionally differentiable functions, Kunh-Tucker necessary conditions, Lagrange multipliers, theorem of the alternative.