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FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

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Abstract

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed.

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Authors and Affiliations

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

    Jesús A. De Loera

  2. Otto-von-Guericke-Universität Magdeburg, FMA/IMO, Universitätsplatz 2, 39106, Magdeburg, Germany

    Raymond Hemmecke, Matthias Köppe & Robert Weismantel

Authors
  1. Jesús A. De Loera
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  2. Raymond Hemmecke
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  3. Matthias Köppe
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  4. Robert Weismantel
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Correspondence to Matthias Köppe.

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De Loera, J.A., Hemmecke, R., Köppe, M. et al. FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension. Math. Program. 115, 273–290 (2008). https://doi.org/10.1007/s10107-007-0175-8

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  • DOI: https://doi.org/10.1007/s10107-007-0175-8

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