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

Xiantao Xiao & Liwei Zhang

DOI: 10.4208/jcm.2009.09-m2674

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 (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.  

  • Keywords

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

  • AMS Subject Headings

90C20, 90C25, 90C90.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-787, author = {Xiantao Xiao and Liwei Zhang}, 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 (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.  

}, 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 AU - Xiantao Xiao & Liwei Zhang 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, Smoothing Newton method, Inverse optimization, Quadratic programming, 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 (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.  

Xiantao Xiao and Liwei Zhang. (2009). 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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