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

Abstract 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 e -(weakly, properly) efficient points of an MOP and ϵ -optimal solutions of the related scalarized problem. For this purpose, the relationships between ϵ ∈ R ≧ and e ∈ 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.

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