4 papers
Approximate Optimal Designs for Multivariate Polynomial Regression
Yohann De Castro, Fabrice Gamboa, Didier Henrion +2
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum…
D-optimal design for multivariate polynomial regression via the Christoffel function and semidefinite relaxations
Yohann De Castro, F Gamboa, D Henrion +2
We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-square…
Improved convergence rates for Lasserre-type hierarchies of upper bounds for box-constrained polynomial optimization
Etienne de Klerk, Roxana Hess, Monique Laurent
We consider the problem of minimizing a given -variate polynomial over the hypercube . An idea introduced by Lasserre, is to find a probability distribution on $[-…
Semidefinite approximations of the polynomial abscissa
Roxana Heß, Didier Henrion, Jean-Bernard Lasserre +1
Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of th…