Coradiant sets and $$\varepsilon $$ ε -efficiency in multiobjective optimization

Abstract

This paper studies $$\varepsilon $$ź-efficiency in multiobjective optimization by using the so-called coradiant sets. Motivated by the nonlinear separation property for cones, a similar separation property for coradiant sets is investigated. A new notion, called Bishop---Phelps coradiant set is introduced and some appropriate properties of this set are studied. This paper also introduces the notions of $$\varepsilon $$ź-dual and augmented $$\varepsilon $$ź-dual for Bishop and Phelps coradiant sets. Using these notions, some scalarization and characterization properties for $$\varepsilon $$ź-efficient and proper $$\varepsilon $$ź-efficient points are proposed.