FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension
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...
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Published in | Mathematical programming Vol. 115; no. 2; pp. 273 - 290 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer-Verlag
01.10.2008
Springer Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | 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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ISSN: | 0025-5610 1436-4646 |
DOI: | 10.1007/s10107-007-0175-8 |