PROXIMAL AUGMENTED LAGRANGIAN AND APPROXIMATE OPTIMAL SOLUTIONS IN NONLINEAR PROGRAMMING

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.