Increase-along-rays property for vector functions

Abstract

In this paper we extend to the vector case the notion of increasing along rays function. The proposed definition is given by means of a nonlinear scalarization through the so-called oriented distance function from a point to a set. We prove that the considered class of functions enjoys properties similar to those holding in the scalar case, with regard to optimization problems, relations with (generalized) convex functions and characterization in terms of Minty type variational inequalities. Key words: generalized convexity, increase-along-rays property, star-shaped set, Minty variational inequality.