Nonlinear augmented Lagrangian for nonconvex multiobjective optimization
Chunrong Chen, T.C.E. Cheng, Shengji Li, Xiaoqi Yang · Journal of Industrial and Management Optimization · 2011
In this paper, based on the orderingrelations induced by a pointed, closed and convex cone with anonempty interior, we propose a nonlinear augmented Lagrangian dualscheme for a nonconvex multiobjective optimization problem byapplying a class of vector-valued nonlinear augmented Lagrangianpenalty functions. We establish the weak and strong duality results,necessary and sufficient conditions for uniformly exact penalizationand exact penalization in the framework of nonlinear augmentedLagrangian. Our results include several ones in the literature asspecial cases.