### Abstract

Original language | English |
---|---|

Pages (from-to) | 3104-3120 |

Journal | SIAM Journal on Optimization |

Volume | 20 |

Issue number | 6 |

Publication status | Published - 2010 |

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*SIAM Journal on Optimization*, vol. 20, no. 6, pp. 3104-3120.

**Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube.** / de Klerk, E.; Laurent, M.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube

AU - de Klerk, E.

AU - Laurent, M.

PY - 2010

Y1 - 2010

N2 - We consider the problem of minimizing a polynomial on the hypercube $[0,1]^n$ and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to the Positivstellensatz of Schmüdgen [Math. Ann., 289 (1991), pp. 203–206]. The main tool we employ is Bernstein approximations of polynomials, which also gives constructive proofs and degree bounds for positivity certificates on the hypercube.

AB - We consider the problem of minimizing a polynomial on the hypercube $[0,1]^n$ and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to the Positivstellensatz of Schmüdgen [Math. Ann., 289 (1991), pp. 203–206]. The main tool we employ is Bernstein approximations of polynomials, which also gives constructive proofs and degree bounds for positivity certificates on the hypercube.

M3 - Article

VL - 20

SP - 3104

EP - 3120

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

SN - 1052-6234

IS - 6

ER -