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论文类型：期刊论文
发表时间：2009-01-01
发表刊物：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
收录刊物：SCIE、EI
卷号：223
期号：1
页面范围：485-498
ISSN号：0377-0427
关键字：Semi-definite quadratic programming; Inverse optimization; Smoothing Newton method
摘要：We consider an inverse problem arising from the semi-definite quadratic programming (SDQP) problem. We represent this problem its a cone-constrained minimization problem and its dual (denoted ISDQD) is a semismoothly differentiable (SC1) convex programming problem with fewer variables than the original one. The Karush-Kuhn-Tucker conditions of the dual problem (ISDQD) can be formulated as a system of semismooth equations which involves the projection onto the cone of positive semi-definite matrices. A smoothing Newton method is given for getting a Karush-Kuhn-Tucker point of ISDQD. The proposed method reeds to compute the directional derivative of the smoothing projector at the corresponding point and to solve one linear system per iteration. The quadratic convergence of the smoothing Newton method is proved under a suitable condition. Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this type of inverse quadratic programming problems. (C) 2008 Elsevier B.V. All rights reserved.