Dra. Vivanco-Orellana, Violeta

Nondegenerate optimality conditions for Pareto and weak Pareto optimal solutions to multiobjective optimization problems with inequality and multi-equality constraints determined by Fréchet differentiable functions are established. First, weak and strong regularity conditions are derived, in order to determine weak Karush–Kuhn–Tucker (positivity of at least one Lagrange multiplier associated with objective functions) and strong Karush–Kuhn–Tucker (positivity of all the Lagrange multipliers associated with objective functions) conditions. Subsequently, the class of problems for which every weak (resp. strong) Karush–Kuhn–Tucker point is weak (resp. strong) Pareto solution is characterized. In addition examples that illustrate our results are presented.

We consider an optimal control problem governed by a system of nonlinear difference equations. We obtain the existence of the optimal control as well as first-order optimality conditions of Pontryagin type by using the Dubovitskii–Milyutin formalism. Also, we give the necessary and sufficient conditions for global optimality.