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Unconstraint global polynomial optimization via Gradient Ideal

Marta Abril Bucero 1 Bernard Mourrain 1 Philippe Trébuchet 2 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
2 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a generalization of Lasserre relaxation method and stops in a finite number of steps. The proposed algorithm combines Border Basis, Moment Matrices and Semidefinite Programming. In the case where the minimum is reached at a finite number of points, it provides a border basis of the minimizer ideal.
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Preprints, Working Papers, ...
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Submitted on : Thursday, March 21, 2013 - 4:46:24 PM
Last modification on : Friday, August 5, 2022 - 3:50:44 AM
Long-term archiving on: : Saturday, June 22, 2013 - 6:35:08 AM


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  • HAL Id : hal-00779666, version 3
  • ARXIV : 1301.5298


Marta Abril Bucero, Bernard Mourrain, Philippe Trébuchet. Unconstraint global polynomial optimization via Gradient Ideal. 2013. ⟨hal-00779666v3⟩



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