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Preprints, Working Papers, ... Year : 2013

Unconstraint global polynomial optimization via Gradient Ideal

Marta Abril Bucero
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Bernard Mourrain
Philippe Trébuchet
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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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Dates and versions

hal-00779666 , version 1 (22-01-2013)
hal-00779666 , version 2 (21-02-2013)
hal-00779666 , version 3 (21-03-2013)



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