Convergence analysis of the augmented Lagrangian method for nonlinear second-order cone optimization problems

摘要

The paper focuses on the convergence rate of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under a set of assumptions of sufficient conditions, including the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second-order sufficient condition, we first study some properties of the augmented Lagrangian and then show that the rate of local convergence of the augmented Lagrangian method is proportional to 1/tau, where the penalty parameter tau is not less than a threshold (tau) over cap > 0. (c) 2006 Elsevier Ltd. All rights reserved.