### Global polynomial optimization with Moment Matrices and Border Basis

Abril-Bucero, M *(INRIA Sophia Antipolis)*

Thursday 18 July 2013, 10:30-11:00

Seminar Room 1, Newton Institute

#### Abstract

Optimization appears in many areas of Scientific Computing, since the solution of a problem can often be described as the minimum of an optimization problem. We describe a new method to compute the global 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.

#### Presentation

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