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The nearest point problem in a polyhedral set and its extensions


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  • Zhe Liu


  • Yahya Fathi


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    In this paper we investigate the relationship between the nearest point problem in a polyhedral cone and the nearest point problem in a polyhedral set, and use this relationship to devise an effective method for solving the latter using an existing algorithm for the former. We then show that this approach can be employed to minimize any strictly convex quadratic function over a polyhedral set. Through a computational experiment we evaluate the effectiveness of this approach and show that for a collection of randomly generated instances this approach is more effective than other existing methods for solving these problems. Copyright Springer Science+Business Media, LLC 2012

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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 53 (2012)
    Issue (Month): 1 (September)
    Pages: 115-130

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    Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:115-130

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    Keywords: Quadratic programming; Pos cone; Projection face; Active constraint;


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    1. Anstreicher, K.M. & Hertog, D. den & Roos, C. & Terlaky, T., 1993. "A long-step barrier method for convex quadratic programming," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377766, Tilburg University.
    2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    3. Zhe Liu & Yahya Fathi, 2011. "An active index algorithm for the nearest point problem in a polyhedral cone," Computational Optimization and Applications, Springer, vol. 49(3), pages 435-456, July.
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