The KL Property Of The Augmented Lagrange Function Of The Second-Order Cone Programming With Linear Constraints And The Bregman Alternating Direction Method With Multipliers

The second-order cone programming is widely used in practical problems such as automatic control and signal processing,so it is of great practical significance to explore efficient methods for solving the second-order cone programming.At present,some theoretical achievements have been made in the study of second-order cone programming,and the main solving methods include the smooth Newton method,the inner point method and the alternating direction method of multipliers.In this paper,we study the Kurdyka-Lojasiewicz property of the augmented Lagrange function in the second-order cone programming with linear constraints and the Bregman alternating direction method with multipliers.Firstly,this paper introduces the research status of the second-order cone programming,the alternating direction method of multipliers and the Kurdyka-Lojasiewicz property.Secondly,we present the related concepts of the second-order cone,the optimality conditions of the second-order cone programming and the basic knowledge of the metric subregularity.The third part studies the Kurdyka-Lojasiewicz property of the augmented Lagrange function for the second-order cone programming with linear constraints,based on which we prove the KurdykaLojasiewicz property of the sum function of the augmented Lagrange function and the Bregman function.Finally,we design the Bregman alternating direction method with multipliers for the second-order cone programming with linear constraints,and analyze its convergence based on the Kurdyka-Lojasiewicz property,and then show the effectiveness of the method through numerical experiments.