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arXiv · 0706.2354

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

Jesús A. De Loera·Raymond Hemmecke·Matthias Köppe·Robert Weismantel
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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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Jesús A. De Loera, Raymond Hemmecke, Matthias Köppe, Robert Weismantel. 2007-06-15. FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension. https://doi.org/10.1007/s10107-007-0175-8

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