[Mat08] Emlékeztető - BME Optimalizálás Szeminárium

[Csilla Majoros]

*Meghívó*

Szeretettel várunk minden kedves érdeklődőt a BME
Optimalizálás Szemináriumán!


Az előadás részletei:

*május 21. (csütörtök), 14.15, H306*

*Etienne de Klerk** (**Tilburg University*
*):*
Convergence analysis for Lasserre's measure-based hierarchy of upper
bounds for polynomial optimization

*Abstract*:
We consider the problem of minimizing  a continuous function $f$  over
a compact set $K$. We analyze a hierarchy of  upper bounds proposed by
Lasserre in [{\em SIAM J. Optim.} $21(3)$ $(2011)$, pp.
$864-885$],obtained by searching for an optimal probability density
function $h$ on $K$ which is a sum of squares of polynomials,so that
the expectation $\int_{\bK} f(x)h(x)dx$ is minimized. We show that the
rate of convergence is $O(1/\sqrt{r})$, where $2r$ is the degree bound
on the density function. This analysis applies to the case when $f$ is
Lipschitz continuous and   $\bK$ is a  full-dimensional  compact set
satisfying some boundary condition (which is satisfied, e.g.,  for
convex sets).The $r$th upper bound in the hierarchy may be computed
using semidefinite programming if $f$ is a polynomial of degree
$d$,and if all moments of order up to $2r+d$ of the Lebesgue measure
on $\bK$ are known, which holds for example if $\bK$ is a simplex,
hypercube, or a Euclidean ball.

Joint work with Monique Laurent and Zhao Sun.
Preprint at: http://arxiv.org/abs/1411.6867



Üdvözlettel,

Majoros Csilla
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