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In this paper, we describe a new method to compute the minimum of a realpolynomial function and the ideal defining the points which minimize thispolynomial function, assuming that the minimizer ideal is zero-dimensional. Ourmethod is a generalization of Lasserre relaxation method and stops in a finitenumber of steps. The proposed algorithm combines Border Basis, Moment Matricesand Semidefinite Programming. In the case where the minimum is reached at afinite number of points, it provides a border basis of the minimizer ideal.

Unconstraint global polynomial optimization via Gradient Ideal