Volume 27, Issue 6
Solving a Class of Inverse QP Problems by a Smoothing Newton Method

Xiantao Xiao & Liwei Zhang

J. Comp. Math., 27 (2009), pp. 787-801.

Published online: 2009-12

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  • Abstract

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 (SC1) convex programming problem with fewer variables than the original one. In this paper a smoothing New- ton 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.  

  • Keywords

Fischer-Burmeister function Smoothing Newton method Inverse optimization Quadratic programming Convergence rate

  • AMS Subject Headings

90C20 90C25 90C90.

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COPYRIGHT: © Global Science Press

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@Article{JCM-27-787, author = {}, title = {Solving a Class of Inverse QP Problems by a Smoothing Newton Method}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {6}, pages = {787--801}, abstract = {

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 (SC1) convex programming problem with fewer variables than the original one. In this paper a smoothing New- ton 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.  

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m2674}, url = {http://global-sci.org/intro/article_detail/jcm/8603.html} }
TY - JOUR T1 - Solving a Class of Inverse QP Problems by a Smoothing Newton Method JO - Journal of Computational Mathematics VL - 6 SP - 787 EP - 801 PY - 2009 DA - 2009/12 SN - 27 DO - http://doi.org/10.4208/jcm.2009.09-m2674 UR - https://global-sci.org/intro/article_detail/jcm/8603.html KW - Fischer-Burmeister function KW - Smoothing Newton method KW - Inverse optimization KW - Quadratic programming KW - Convergence rate AB -

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 (SC1) convex programming problem with fewer variables than the original one. In this paper a smoothing New- ton 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.  

Xiantao Xiao & Liwei Zhang. (2019). Solving a Class of Inverse QP Problems by a Smoothing Newton Method. Journal of Computational Mathematics. 27 (6). 787-801. doi:10.4208/jcm.2009.09-m2674
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