Analysis on a Superlinearly Convergent Augmented Lagrangian Method  

作　　者：Ya Xiang YUAN 

机构地区：[1]State Key Laboratory of Scientific/Engineering Computing,Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Acta Mathematica Sinica,English Series》2014年第1期1-10,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.10831006,11021101);by CAS(Grant No.kjcx-yw-s7)

摘　　要：The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems.However,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear convergence.In this paper,we study an update technique based on second order information and prove that superlinear convergence can be obtained.Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems.However,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear convergence.In this paper,we study an update technique based on second order information and prove that superlinear convergence can be obtained.Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.

关 键 词：Nonlinearly constrained optimization augmented Lagrange function Lagrange multiplier convergence 

分 类 号：O174[理学—数学]