Scalarizations for Approximate Quasi Efficient Solutions in Multiobjective Optimization Problems

Abstract

In this paper, by reviewing two standard scalarization techniques, a new necessary and sufficient condition for characterizing \((\varepsilon ,\bar{\varepsilon })\)-quasi (weakly) efficient solutions of multiobjective optimization problems is presented. The proposed procedure for the computation of \((\varepsilon ,\bar{\varepsilon })\)-quasi efficient solutions is given. Note that all of the provided results are established without any convexity assumptions on the problem under consideration. And our results extend several corresponding results in multiobjective optimization.