Preprint series: 04-17, Reports on Optimization and Stochastics

MSC:

90C48 Programming in abstract spaces

52A41 Convex functions and convex programs, See also {26B25,

90C29 Multi-objective and goal programming; vector optimization

Abstract: The aim of this paper is to develop a conjugate duality theory, based on set relation approach, for convex set-valued maps. The basic idea is to understand a convex set-valued map as a function with values in the space of closed convex subsets of R^p. The usual inclusion of sets provides a natural ordering relation in this space. Infimum and supremum with respect to this ordering relation can be expressed with the aid of union and intersection. Our main result is a strong duality assertion formulated along the lines of classical duality theorems for extended real-valued convex functions.

Keywords: set-valued optimization; set relations; duality; power structures; embedding of convex sets

Upload: 2004-04-15

Update: 2005 -01 -11