Multi-objective infinite programming

Using the theory of abstract optimization problems in infinite-dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi-objective infinite programming problem. Sufficient conditions are given under invexity assumptions. We generalize the notion of KKT-invexity for the multi-objective infinite problem and show that this notion is a necessary and sufficient condition for every vector KKT solution to be a weakly efficient solution. Moreover, we develop a theorem of the alternative, useful for proving some of our results.