Nonlinear Lagrangian for multiobjective optimization and applications to duality and exact penalization. (English) Zbl 1036.90062
The authors introduce vector-valued nonlinear Lagrangian and penalty functions and formulate nonlinear Lagrangian dual problems and nonlinear penalty problems for (nonconvex) multiobjective constrained optimization problems. They obtain weak and strong duality and saddle point results.
Conditions are given which are necessary and sufficient for the existence of a global (local) exact penalty parameter for nonlinear penalty multiobjective optimization problems.
Conditions are given which are necessary and sufficient for the existence of a global (local) exact penalty parameter for nonlinear penalty multiobjective optimization problems.
Reviewer: Francisco Guerra Vazquez (Puebla)
MSC:
90C29 | Multi-objective and goal programming |
90C46 | Optimality conditions and duality in mathematical programming |