Using the approximation theoretic notion of norming set, we compute(1−eps)-approximations to the global minimum of arbitrary n-th degree polynomials on the sphere, by discrete minimization on approximately 3.2n^2/eps trigonometric grid points, or 2n^2/eps quasi-uniform points. The same error size is attained by approximately 6.5n^2/eps trigonometric grid points on the torus.
Global polynomial optimization by norming sets on sphere and torus
Vianello M.
2018
Abstract
Using the approximation theoretic notion of norming set, we compute(1−eps)-approximations to the global minimum of arbitrary n-th degree polynomials on the sphere, by discrete minimization on approximately 3.2n^2/eps trigonometric grid points, or 2n^2/eps quasi-uniform points. The same error size is attained by approximately 6.5n^2/eps trigonometric grid points on the torus.
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