Duality for the Multiobjective Location Model Involving Sets as Existing Facilities

Abstract

In this paper we consider the optimization problem with a multiobjective composed convex function as objective function, namely, being a composite of a convex and componentwise increasing vector function with a convex vector function. By the conjugacy approach, we obtain a dual problem for it. The existence of weak and strong duality is proved. Using this general result, we introduce the dual problem for the multiobjective location problem in a general normed space, in which the existing facilities are represented by sets of points. The biobjective Weber-minimax problem, the multiobjective Weber problem and the multiobjective minimax problem with demand sets are studied as particular cases of this problem.