A Perturbation approach for an inverse quadratic programming problem

doi:10.1007/s00186-010-0323-4

科研成果详情

题名	A Perturbation approach for an inverse quadratic programming problem
作者	Zhang，Jianzhong 1; Zhang，Liwei 2; Xiao，Xiantao 2
发表日期	2010
发表期刊	Mathematical Methods of Operations Research
ISSN/eISSN	1432-2994
卷号	72 期号:3 页码:379-404
摘要	We consider an inverse quadratic programming (QP) problem in which the parameters in both the objective function and the constraint set of a given QP problem need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a linear complementarity constrained minimization problem with a positive semidefinite cone constraint. With the help of duality theory, we reformulate this problem as a linear complementarity constrained semismoothly differentiable (SC ) optimization problem with fewer variables than the original one. We propose a perturbation approach to solve the reformulated problem and demonstrate its global convergence. An inexact Newton method is constructed to solve the perturbed problem and its global convergence and local quadratic convergence rate are shown. As the objective function of the problem is a SC function involving the projection operator onto the cone of positively semi-definite symmetric matrices, the analysis requires an implicit function theorem for semismooth functions as well as properties of the projection operator in the symmetric-matrix space. Since an approximate proximal point is required in the inexact Newton method, we also give a Newton method to obtain it. Finally we report our numerical results showing that the proposed approach is quite effective. © 2010 Springer-Verlag.
关键词	Inexact Newton method Inverse optimization Perturbation approach Quadratic programming
DOI	10.1007/s00186-010-0323-4
URL	查看来源
语种	英语English
Scopus入藏号	2-s2.0-78650694305
引用统计	被引频次：8[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://repository.uic.edu.cn/handle/39GCC9TT/6624
专题	北师香港浸会大学
通讯作者	Xiao，Xiantao
作者单位	1.United International College,Beijing Normal University-HongKong Baptist University,Zhuhai,China 2.School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China
第一作者单位	北师香港浸会大学
推荐引用方式 GB/T 7714	Zhang，Jianzhong,Zhang，Liwei,Xiao，Xiantao. A Perturbation approach for an inverse quadratic programming problem[J]. Mathematical Methods of Operations Research, 2010, 72(3): 379-404.
APA	Zhang，Jianzhong, Zhang，Liwei, & Xiao，Xiantao. (2010). A Perturbation approach for an inverse quadratic programming problem. Mathematical Methods of Operations Research, 72(3), 379-404.
MLA	Zhang，Jianzhong,et al."A Perturbation approach for an inverse quadratic programming problem". Mathematical Methods of Operations Research 72.3(2010): 379-404.