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Quadratic reformulations of nonlinear binaryoptimization problems

Anthony, Martin and Boros, Endre and Crama, Yves and Gruber, Aritanan (2017) Quadratic reformulations of nonlinear binaryoptimization problems. Mathematical Programming, 162 (1). pp. 115-144. ISSN 0025-5610

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Identification Number: 10.1007/s10107-016-1032-4

Abstract

Very large nonlinear unconstrained binary optimization problems arise in a broad array of applications. Several exact or heuristic techniques have proved quite successful for solving many of these problems when the objective function is a quadratic polynomial. However, no similarly efficient methods are available for the higher degree case. Since high degree objectives are becoming increasingly important in certain application areas, such as computer vision, various techniques have been recently developed to reduce the general case to the quadratic one, at the cost of increasing the number of variables. In this paper we initiate a systematic study of these quadratization approaches. We provide tight lower and upper bounds on the number of auxiliary variables needed in the worst-case for general objective functions, for bounded-degree functions, and for a restricted class of quadratizations. Our upper bounds are constructive, thus yielding new quadratization procedures. Finally, we completely characterize all ``minimal'' quadratizations of negative monomials.

Item Type: Article
Official URL: http://link.springer.com/
Additional Information: © 2016 Springer International Publishing AG
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Q Science > QD Chemistry
Sets: Departments > Mathematics
Date Deposited: 23 May 2016 09:53
Last Modified: 01 Nov 2017 16:15
Projects: IIS-1161476, P7/36, BEX-2387050/15061676, 2014/23269-8
Funders: National Science Foundation, Interuniversity Attraction Poles Programme, Fund for Scientific Research, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Sao Paulo Science Foundation
URI: http://eprints.lse.ac.uk/id/eprint/66580

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