5 papers · 1 filter
Squared polynomial approximation kernels for the hypercube: improved error bounds and implications for Lasserre hierarchies
Sander Gribling, Etienne de Klerk, Juan C. Vera
We propose a new family of polynomial approximation kernels for approximating nonnegative polynomials on the hypercube . Our Kernels produce polynomial sums-of-squares of…
Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube
Sander Gribling, Etienne de Klerk, Juan Vera
We revisit the problem of minimizing a given polynomial on the hypercube . Lasserre's hierarchy (also known as the moment- or sum-of-squares hierarchy) provides a seq…
Least multivariate Chebyshev polynomials on diagonally determined sets
Mareike Dressler, Simon Foucart, Mioara Joldes +3
We consider a new multivariate generalization of the classical monic (univariate) Chebyshev polynomial that minimizes the uniform norm on the interval . Let be the…
The link between -norm approximation and effective Positivstellensatze for the hypercube
Etienne de Klerk, Juan Vera Lizcano
The Schmüdgen's Positivstellensatz gives a certificate to verify positivity of a strictly positive polynomial on a compact, basic, semi-algebraic set $\mathbf{K} \subset \math…
Optimization-Aided Construction of Multivariate Chebyshev Polynomials
Mareike Dressler, Simon Foucart, Mioara Joldes +3
This article is concerned with an extension of univariate Chebyshev polynomials of the first kind to the multivariate setting, where one chases best approximants to specific monomi…