Alternative Theorems and Necessary Optimality Conditions for Directionally Difierentiable Multiobjective Programs
B. JimÊenez, Vicente Novo · 2002
In this paper we study, in a unifled way, some alternative theorems that involve linear and sublinear functions between flnite dimensional spaces and a convex set, and we propose several generalizations of them. These theorems are applied to obtain, under difierent constraint qualiflcations, several necessary conditions for a point to be Pareto optimum, both Fritz John and Kuhn-Tucker type, in multiobjective programming problems which are deflned by directionally difierentiable functions and which include three types of constraints: inequality, equality and set constraints. In particular, these necessary conditions are applicable to convex programs and to difierentiable programs.