SOLVING A CLASS OF INVERSE QP PROBLEMS BY A SMOOTHING NEWTON METHOD

作     者：Xiantao Xiao Liwei Zhang 

作者机构：Department of Applied Mathematics Dalian University of Technology Dalian 116024 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2009年第27卷第6期

页      面：787-801页

核心收录：

学科分类：080903[工学-微电子学与固体电子学] 07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China under project No. 10771026 by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China 

主　　题：Fischer-Burmeister function Smoothing Newton method Inverse optimization Quadratic programming Convergence rate. 

摘      要：We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual （denoted IQD（A, b）） is a semismoothly differentiable （SC^1） convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD（A, b）. The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.