On approximating weakly/properly efficient solutions in multi-objective programming

This paper deals with approximate solutions of general (that is, without any convexity assumption) multi-objective optimization problems (MOPs). In this text, by reviewing some standard scalarization techniques we are interested in finding the relationships between εε-(weakly, properly) efficient points of an MOP and ϵϵ-optimal solutions of the related scalarized problem. For this purpose, the relationships between ϵ∈R≧ϵ∈R≧ and ε∈R≧m, for a single objective and multi-objective problems, respectively, are analyzed. In fact, necessary and/or sufficient conditions for approximating (weakly, properly) efficient points of a general MOP via approximate solutions of the scalarized problems are obtained.