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math.OC2025
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…
math.OC2025
Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre +1
We consider polynomial optimization problems (POP) on a semialgebraic set contained in the nonnegative orthant (every POP on a compact set can be put in this format by a simple tra…
math.OC2024
A Generalized Pell's equation for a class of multivariate orthogonal polynomials
Jean-Bernard Lasserre, Yuan Xu
We extend the polynomial Pell's equation satisfied by univariate Chebyshev polynomials on [--1, 1] from one variable to several variables, using orthogonal polynomials on regular d…