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arXiv · 1301.5298

Unconstraint global polynomial optimization via Gradient Ideal

Marta Abril Bucero·Bernard Mourrain·Philippe Trebuchet
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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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Marta Abril Bucero, Bernard Mourrain, Philippe Trebuchet. 2013-03-21. Unconstraint global polynomial optimization via Gradient Ideal. https://arxiv.org/abs/1301.5298

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