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, 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [32 references]  Display  Hide  Download

https://hal.inria.fr/hal-00779666
Contributor : Marta Abril Bucero <>
Submitted on : Thursday, March 21, 2013 - 4:46:24 PM
Last modification on : Thursday, March 21, 2019 - 1:06:11 PM
Long-term archiving on : Saturday, June 22, 2013 - 6:35:08 AM

Files

optimization1.pdf
Files produced by the author(s)

Identifiers

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

Citation

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

Share

Metrics

Record views

647

Files downloads

348