Pascoletti-Serafini scalarization and vector optimization with a variable ordering structure

Abstract

In this paper, optimality concepts for vector optimization problems with a variable ordering structure are considered. The notion of Pascoletti-Serafini scalarization for the vector optimization problems is extended. Then, some relations between optimal elements of the vector optimization problem and efficient solutions of scalarized problem are obtained. Also, by using the generalized Pascoletti-Serafini scalarization method, nonsmooth variational-like inequalities are defined and their relations with the scalarized optimization problems are studied.

Subject Classification:

• (2010) 49J52
• 90C26
• 49J40

Keywords:

• Nonsmooth variational-like inequalities
• Vector optimization
• Variable ordering structures
• Scalarization