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

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

2007-06-15

arxiv.org/abs/0706.2354v1

Mathematics

Optimization and Control

16 pages, 4 figures; to appear in Mathematical Programming

Scientific paper

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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