Abstract
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.
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This work was supported by the National Natural Science Foundation of China grants 10571106, 10471159.
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Liu, Q., Tang, W.M. & Yang, X.M. Properties of saddle points for generalized augmented Lagrangian. Math Meth Oper Res 69, 111–124 (2009). https://doi.org/10.1007/s00186-008-0213-1
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DOI: https://doi.org/10.1007/s00186-008-0213-1