仿射变换内点Levenberg-Marquardt法解KKT系统(英文)  

Affine scaling interior Levenberg-Marquardt method for KKT systems

作　　者：王云娟[1] 朱德通[2] 

机构地区：[1]上海立信会计学院数学与信息学院,上海201620 [2]上海师范大学商学院,上海200234

出　　处：《运筹学学报》2013年第2期89-106,共18页Operations Research Transactions

基　　金：supported by The National Natural Science Foundation of China(No.10871130)

摘　　要：提供了一类新的结合非单调内点回代线搜索技术的仿射变换Levenberg-Marquardt法解Karush-Kuhn-Tucker(KKT)系统。基于由KKT系统转化得到的等价的部分变量具有非负约束的最小化问题,建立了Levenberg-Marquardt方程。证明了算法不仅具有整体收敛性,而且在合理的假设条件下,算法具有超线性收敛速率。数值结果验证了算法的实际有效性。We develop and analyze a new affine scaling Levenberg-Marquardt method with nonmonotonic interior backtracking line search technique for solving Karush-Kuhncker （KKT） system. By transforming the KKT system into an equivalent minimization problem with nonnegativity constraints on some of the variables, we establish the Levenberg-Marquardt equation based on this reformulation. Theoretical analysis are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergent rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

关 键 词：KKT系统 Levenberg—Marquardt法 仿射变换 内点 收敛 

分 类 号：O221.2[理学—运筹学与控制论]