66 citations · 187 across the 28 of their papers we have counts for
31 papers
Further analysis and extension of the higher-order Newton method of Ahmadi, Chaudhry, and Zhang
Lucas ter Voert, Etienne de Klerk
We extend a th-order Newton method for unconstrained optimization by Ahmadi, Chaudhry, and Zhang [Advances in Mathematics, 452:109808] to optimization with SOS-convex polynomial…
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…
On the convergence rate of the boosted Difference-of-Convex Algorithm (DCA)
Hadi Abbaszadehpeivasti, Etienne de Klerk, Adrien Taylor
The difference-of-convex algorithm (DCA) is a well-established nonlinear programming technique that solves successive convex optimization problems. These sub-problems are obtained…
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…
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…