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Quadratic reformulations of nonlinear binary optimization problems

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

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


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
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Additional Information: © 2016 Springer International Publishing AG
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Q Science > QD Chemistry
Date Deposited: 23 May 2016 09:53
Last Modified: 03 Jul 2024 22:54
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

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