Coderivatives and Aubin property of efficient point and efficient solution set-valued maps in parametric vector optimization

Abstract

Abstract The aim of this paper is computing the coderivatives of efficient point and efficient solution set-valued maps in a parametric vector optimization problem. By using a method different from the existing literature we establish an upper estimate and explicit expression for the coderivatives of an efficient point set-valued map where the independent variable can take values in the whole space. As an application, we give some characterizations on the Aubin property of an efficient point map and an explicit expression of the coderivative for an efficient solution map. We provide several examples illustrating the main results.

Keywords

• Parametric vector optimization
• Efficient point set-valued map
• Efficient solution set-valued map
• (Fréchet) coderivative
• Aubin property