Superlinear Convergence of Affine Scaling Interior Point Newton Method for Linear Inequality Constrained Minimization without Strict Complementarity

作     者：De-tong Zhu 

作者机构：Business College Shanghai Normal University Shanghai 200234 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2009年第25卷第2期

页      面：183-194页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 0835[工学-软件工程] 0701[理学-数学] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported by the National Natural Science Foundation of China(No.10871130) the Ph.D.Foundation Grant (0527003) of Chinese Education Ministry,the Shanghai Leading Academic Discipline Project(T0401) the Science Foundation Grant(05DZ11) of Shanghai Education Committee 

主　　题：Interior method affine scaling strict complementarity 

摘      要：In this paper we extend and improve the classical affine scaling interior-point Newton method for solving nonlinear optimization subject to linear inequality constraints in the absence of the strict complementarity assumption. Introducing a computationally efficient technique and employing an identification function for the definition of the new affine scaling matrix, we propose and analyze a new affine scaling interior-point Newton method which improves the Coleman and Li affine sealing matrix in [2] for solving the linear inequlity constrained optimization. Local superlinear and quadratical convergence of the proposed algorithm is established under the strong second order sufficiency condition without assuming strict complementarity of the solution.