The nearest point problem in a polyhedral set and its extensions

Authors:
Zhe Liu;Yahya Fathi
Affiliations:
Graduate Program in Operations Research, North Carolina State University, Raleigh, USA 27695;Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, USA 27695
Venue:
Computational Optimization and Applications
Year:
2012

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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.