We show that Lasserre measure-based hierarchies for polynomial optimization can be implemented by directly computing the discrete minimum at a suitable set of algebraic quadrature nodes. The sampling cardinality can be much lower than in other approaches based on grids or norming meshes. All the vast literature on multivariate algebraic quadrature becomes in such a way relevant to polynomial optimization
Quadrature-based polynomial optimization
Martinez, Angeles;Piazzon, Federico;Sommariva, Alvise;Vianello, Marco
2020
Abstract
We show that Lasserre measure-based hierarchies for polynomial optimization can be implemented by directly computing the discrete minimum at a suitable set of algebraic quadrature nodes. The sampling cardinality can be much lower than in other approaches based on grids or norming meshes. All the vast literature on multivariate algebraic quadrature becomes in such a way relevant to polynomial optimization
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