Local Saddle Points Theory of a New Augmented Lagrangians
In connection with Problem (P) with both the equality constraints and inequality constraints, we introduce a new augmented lagrangian function. We establish the existence of local saddle point under the weaker sufficient second order condition, discuss the relationships between local optimal solution of the primal problem and local saddle point of the augmented lagrangian function.
Donald C. Wunsch II, Honghua Tan, Dehuai Zeng, Qi Luo
W. L. Zhao et al., "Local Saddle Points Theory of a New Augmented Lagrangians", Advanced Materials Research, Vols. 121-122, pp. 123-127, 2010