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This document investigates polyhedral approximations to the cone of nonnegative polynomials, demonstrating that constant ratio approximations in dense cases require exponentially many facets. It establishes that for fixed dimensions, there exist approximations with a polynomial number of facets in structured subspaces of polynomials. The study employs convex geometric methods and discusses a randomized approach to polyhedral approximation, highlighting the complexity of nonnegative cone membership problems.

Author

jkljlj

Language

EN