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 $ϵ$ ‐(weakly, properly) efficient points of an MOP and $ϵ$ ‐optimal solutions of the related scalarized problem. For this purpose, the relationships between $ϵ\in {‐{R}}_{\geqq }$ and $ϵ\in {‐{R}}_{\geqq }^m$ , 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.