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Computation with Polynomial Equations and Inequalities Arising in Combinatorial Optimization

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Book cover Mixed Integer Nonlinear Programming

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 154))

Abstract

This is a survey of a recent methodology to solve systems of polynomial equations and inequalities for problems arising in combinatorial optimization. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear algebra or semidefinite programming relaxations of many kinds of feasibility or optimization questions.

AMS(MOS) subject classifications. 90C27, 90C22, 68W05.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Davis, Davis, CA, 95616, USA

    Jesus A. De Loera & Peter N. Malkin

  2. Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Pablo A. Parrilo

Authors
  1. Jesus A. De Loera
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  2. Peter N. Malkin
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  3. Pablo A. Parrilo
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Corresponding author

Correspondence to Jesus A. De Loera .

Editor information

Editors and Affiliations

  1. , College of Engineering, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, 48109, Michigan, USA

    Jon Lee

  2. , Mathematics and Computer Science, Argonne National Laboratory, Argonne, 60439, Illinois, USA

    Sven Leyffer

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De Loera, J.A., Malkin, P.N., Parrilo, P.A. (2012). Computation with Polynomial Equations and Inequalities Arising in Combinatorial Optimization. In: Lee, J., Leyffer, S. (eds) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol 154. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1927-3_16

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