Further results on quasi efficient solutions in multiobjective optimization

Abstract

This work focuses on quasi efficient solutions of a vector optimization problem. Namely, it is assumed the objective function to map values between finite dimensional spaces and the ordering in the final space is defined by a pointed convex cone. In this setting, several new concepts of quasi efficient solutions are introduced and their basic properties are obtained. After that, it is studied their limit behavior in order to deduce when they approximate well other kind of efficient solutions of the problem. Finally, in convex problems, linear scalarization results are stated that relate the introduced quasi efficient solutions with solutions of scalar optimization problems. The concepts and results of the paper extend and clarify several ones of the recent literature