Inexact Augmented Lagrangian Method For Second-Order Cone Constrained Optimization Problems

In this paper,we focus on the second-order cone constrained optimization prob-lem,and study the convergence and convergence rate of the exact and inexact augmented Lagrange method.Firstly,we establish the KKT system and define the Lagrange multiplier by using the first derivative of the augmented Lagrange function.Based on the KKT system,the framework of the inexact augmented La-grange algorithm is given.Then,under the Robinson constrained property,the calm property of the generalized equation and the second-order sufficient condition,the convergence and convergence speed of the algorithm are proved.When the penalty parameter is sufficiently large,the dual sequence generated by the algorith-m iteration is linearly convergent.Further,when the penalty parameter approaches infinity,the convergence rate is superlinear.