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The nearest point problem in a polyhedral set and its extensions

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  • Zhe Liu
  • Yahya Fathi

Abstract

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

Suggested Citation

  • Zhe Liu & Yahya Fathi, 2012. "The nearest point problem in a polyhedral set and its extensions," Computational Optimization and Applications, Springer, vol. 53(1), pages 115-130, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:115-130
    DOI: 10.1007/s10589-011-9448-5
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    References listed on IDEAS

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    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. 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.
    3. V. Ruggiero & L. Zanni, 2000. "A Modified Projection Algorithm for Large Strictly-Convex Quadratic Programs," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 255-279, February.
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