Duality for Set-Valued Multiobjective Optimization Problems, Part 1: Mathematical Programming

The duality of multiobjective problems is studied with the help of the apparatus of conjugate set-valued mappings introduced by the author. In this paper (Part 1), a duality theory is developed for set-valued mappings, which is then used to derive dual relations for some general multiobjective optimization problems which include convex programming and optimal control problems. Using this result, in the companion paper (Part 2), duality theorems are proved for multiobjective quasilinear and linear optimal control problems. The theory is applied to get dual relations for some multiobjective optimal control problem.