Characterization of Weakly Efficient Solutions for Non-Regular Multiobjective Programming Problems with Inequality-Type Constraints

Necessary conditions of optimality are presented for weakly efficient solutions to multiobjective minimization problems with inequality-type constraints. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions and they are based on the concept of 2-regularity introduced by Izmailov. In general, the optimality conditions do not provide the complete weak Pareto optimal set, so 2-KKT-pseudoinvex problems are defined. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all weakly efficient solutions based on the optimality conditions and it is the weakest one.