Title of Paper:A smoothing Newton method for a type of inverse semi-definite quadratic programming problem

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Date of Publication:2009-01-01

Journal:JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Included Journals:SCIE、EI

Volume:223

Issue:1

Page Number:485-498

ISSN No.:0377-0427

Key Words:Semi-definite quadratic programming; Inverse optimization; Smoothing Newton method

Abstract: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.