Proximal Proper Saddle Points in Set-Valued Optimization

A new notion of saddle point, namely proximal proper saddle point is introduced in terms of a Lagrangian map associated with a set-valued optimization problem for which an existence criterion is obtained. It is also observed that this saddle point is not related to some of the well-known saddle points. A saddle point type optimality criterion is derived for optimality in terms of proximal proper minimizers.