Generalized quasiconvex set-valued maps

Abstract

The aim of this paper is to introduce a concept of quasiconvexity for set-valued maps in a general framework, by only considering an abstract convexity structure in the domain and an arbitrary binary relation in the codomain. It is shown that this concept can be characterized in terms of usual quasiconvexity of certain real-valued functions. In particular, we focus on cone-quasiconvex set-valued maps with values in a partially ordered vector space.

Keywords

• generalized quasiconvexity
• set-valued maps
• scalarization