Roxana Hess

D-OPTIMAL DESIGN FOR MULTIVARIATE POLYNOMIAL REGRESSION VIA THE CHRISTOFFEL FUNCTION AND SEMIDEFINITE RELAXATIONS

  • Yohann De Castro
  • Didier Henrion
  • Jean-Bernard Lasserre
  • Fabrice Gamboa
  • Roxana Hess
    • Categories Semi-definite Programming, Statistics

    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. Article … Read more

    Improved convergence rates for Lasserre-type hierarchies of upper bounds for box-constrained polynomial optimization

  • Etienne de Klerk
  • Monique Laurent
  • Roxana Hess
    • Categories Semi-definite Programming Tags , , , , ,

    We consider the problem of minimizing a given $n$-variate polynomial $f$ over the hypercube $[-1,1]^n$. An idea introduced by Lasserre, is to find a probability distribution on $[-1,1]^n$ with polynomial density function $h$ (of given degree $r$) that minimizes the expectation $\int_{[-1,1]^n} f(x)h(x)d\mu(x)$, where $d\mu(x)$ is a fixed, finite Borel measure supported on $[-1,1]^n$. It … Read more

    Semidefinite approximations of the polynomial abscissa

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Tiên-So'n Pham
  • Roxana Hess
    • Categories Control Applications, Nonsmooth Optimization, Semi-definite Programming Tags , , , ,

    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 the polynomial coefficients, the abscissa is H\”older continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In … Read more