Multiobjective programming with (p, r)-invexity

A nonlinear multiobjective programming problem is considered where the functions involved are differentiable. In this work, we generalize some scalar optimization theory results making them applicable to vectorial optimization. By using the concept of (p, r)-invexity we give a new characterization of solutions of multiobjective programming problems. To do this, we introduce the definitions of stationary points and Kuhn-Tucker points for multiobjective programming problems. We prove, for unconstrained multiobjective programming problems with (p,r)-invex functions, that the equivalence between optimal solutions and stationary points remains true when several objective functions are optimized instead of one objective function. Moreover, we give two types of Kuhn-Tucker optimality conditions for constrained multiobjective programming problems. For this purpose, we generalize Martin's [16] definition of KT-invex problems to vectorial optimization problems with (p,r)-invex functions.