Optimality and Lagrangian duality for vector optimization of set-valued maps
Jia Ji-hong, Luo Xue-bo · Journal of Northwest University · 2004
Aim In topological vector spaces, the optimization of set-valued maps and Lagrangian type dual problems are studied.MethodsThe concept of genralized subconvexlikeness of single-valued maps is extended to set-valued maps. An alternative theorem is established in topological vector spaces.Then, an optimality necessary conditon for the optimization of set-valued maps is studied using this alternative theorem. A Lagrangian type dual is defined. ResultsAn optimality necessary condition for the optimization of set-valued maps and duality results are established. ConclusionThese results deepen and enrich content of optimization theory.