Properties of saddle points for generalized augmented Lagrangian

For inequality constrained optimization problem, we show the existence of local saddle point of generalized augmented Lagrangian under weak second-order sufficient conditions which are weaker than the second-order sufficient conditions in the literature. We further discuss the existence of global saddle points without requiring the uniqueness of the global optimal solution. This work was supported by the National Natural Science Foundation of China grants 10571106, 10471159.