Optimality Conditions in Directionally Differentiable Pareto Problems with a Set Constraint via Tangent Cones
Bienvenido Jiménez, Vicente Novo · Numerical Functional Analysis and Optimization · 2003
We study a multiobjective optimization problem in with a feasible set defined by inequality and equality constraints and a convex set constraint. All the involved functions are, at least, directionally differentiable. Quasiconvex inequalities are considered. Given these assumptions, an expression for the contingent cone to the feasible set using an extended Mangasarian-Fromovitz constraint qualification is provided. As application, necessary and sufficient optimality conditions of Kuhn-Tucker type are established for a local Pareto minimal point.