An Elementary Approach to Polynomial Optimization on Polynomial Meshes

Marco Vianello (Department of Mathematics Università degli Studi di Padova Via Trieste, 63 - 35121 Padova)

Journal of Mathematical and Fundamental Sciences
Vol. 50 No. 1 (2018)

A polynomial mesh on a multivariate compact set or manifold is a sequence of finite norming sets for polynomials whose norming constant is independent of degree. We apply the recently developed theory of polynomial meshes to an elementary discrete approach for polynomial optimization on nonstandard domains, providing a rigorous (over)estimate of the convergence rate. Examples include surface/solid subregions of sphere or torus, such as caps, lenses, lunes, and slices.