First and second order sufficient conditions for strict minimality in multiobjective programming

In this paper, first and second order sufficient conditions are established for strict local Pareto minima of orders 1 and 2 to multiobjective optimization problems with an arbitrary feasible set and a twice differentiable objective function are provided. For this aim, the concept of support function to a multiobjective problem is introduced, so that the scalar case in particular is contained. The obtained results generalize the classical ones of this case. Furthermore, particularizing to a feasible set defined by equality and inequality constraints, first and second order optimality conditions in primal form as well as dual form (by means of a Lagrange multiplier rule) are obtained.