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 ∈ R= and ε ∈ R= , 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. © 2011 Elsevier Ltd. All rights reserved.