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The nearest point problem in a polyhedral set and its extensions

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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.

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Acknowledgements

This work is partially supported by the NSF grant DMI-0321635 which is gratefully acknowledged. We also would like to express our appreciation to the two anonymous referees for their constructive comments and helpful suggestions.

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Authors and Affiliations

  1. Graduate Program in Operations Research, North Carolina State University, Raleigh, NC, 27695, USA

    Zhe Liu

  2. Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695, USA

    Yahya Fathi

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  1. Zhe Liu
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  2. Yahya Fathi
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Correspondence to Zhe Liu.

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Liu, Z., Fathi, Y. The nearest point problem in a polyhedral set and its extensions. Comput Optim Appl 53, 115–130 (2012). https://doi.org/10.1007/s10589-011-9448-5

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  • DOI: https://doi.org/10.1007/s10589-011-9448-5

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