Convexificators for nonconvex multiobjective optimization problems with uncertain data: robust optimality and duality

In this paper, we investigate robust optimality conditions and duality for a class of nonconvex multiobjective optimization problems with uncertain data in the worst case by the upper semi-regular convexificator. The Fermat principle for a locally Lipschitz function is presented in terms of the upper semi-regular convexificator. We establish robust necessary optimality conditions of the Fritz-John type and KKT type for the uncertain nonconvex multiobjective optimization problems. In addition, robust sufficient optimality conditions as well as saddle point conditions are derived under the generalized $ \hat {\partial }<^>{\ast } $ partial differential *-pseudoquasiconvexity and generalized convexity, respectively. The robust duality relations between the original problem and its mixed robust dual problem are obtained under a generalized pseudoconvexity assumption.

Automated summary

This paper investigates the robust optimality conditions and duality for a class of nonconvex multiobjective optimization problems with uncertain data. The Fermat principle for a locally Lipschitz function is presented using the upper semi-regular convexificator. Robust necessary optimality conditions of the Fritz-John type and KKT type are established for the uncertain nonconvex multiobjective optimization problems. Additionally, robust sufficient optimality conditions and saddle point conditions are derived under the generalized $ \hat {\partial }<^>{\ast } $ partial differential *-pseudoquasiconvexity and generalized convexity, respectively. The robust duality relations between the original problem and its mixed robust dual problem are obtained under a generalized pseudoconvexity assumption.