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

Abstract

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 / τ , where the penalty parameter τ is not less than a threshold τ ˆ > 0 .