Optimization with set relations: conjugate duality
Andreas Löhne · Optimization · 2005
The aim of this article 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 . 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.