117 research outputs found
04401 Abstracts Collection -- Algorithms and Complexity for Continuous
From 26.09.04 to 01.10.04, the Dagstuhl Seminar ``Algorithms and Complexity for Continuous Problems\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial minimization on the sphere
We study the convergence rate of a hierarchy of upper bounds for polynomial
minimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp.
864-885], for the special case when the feasible set is the unit (hyper)sphere.
The upper bound at level r of the hierarchy is defined as the minimal expected
value of the polynomial over all probability distributions on the sphere, when
the probability density function is a sum-of-squares polynomial of degree at
most 2r with respect to the surface measure.
We show that the exact rate of convergence is Theta(1/r^2), and explore the
implications for the related rate of convergence for the generalized problem of
moments on the sphere.Comment: 14 pages, 2 figure
A Riemannian-Stein Kernel Method
This paper presents a theoretical analysis of numerical integration based on
interpolation with a Stein kernel. In particular, the case of integrals with
respect to a posterior distribution supported on a general Riemannian manifold
is considered and the asymptotic convergence of the estimator in this context
is established. Our results are considerably stronger than those previously
reported, in that the optimal rate of convergence is established under a basic
Sobolev-type assumption on the integrand. The theoretical results are
empirically verified on
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