Title: D-optimal design for multivariate polynomial regression via the Christoffel function and semidefinite relaxations,
Abstract: 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-squares hierarchy of semidefinite programming problems
to solve numerically and approximately the optimal design problem. The geometry
of the design is recovered with semidefinite programming duality theory and the
Christoffel polynomial.