The Multiobjective Optimization Problem of Set Function
Kensuke Tanaka, Yukihiro Maruyama · Journal of Information and Optimization Sciences · 1984
The multiobjective optimization problem of a set function defined on a σ-algebra If in a finite atomless measure space (X, II, m) is investigated. A constrained local minimum is formulated and its necessary conditions are derived. Also, the sufficient conditions of a constrained local lower efficient point are given. Further, a necessary condition of a constrained minimum is shown in a form of a saddle point of a Lagrangian set function and a theorem for Lagrangian duality is given.