N&O seminar: Lucas Slot (CWI)

Everyone is welcome to attend the N&O lecture of Lucas Slot with the title 'Improved convergence analysis of Lasserre's measure-based upper bounds for polynomial minimization on compact sets'.
  • What Networks & Optimization English Seminars
  • When 29-05-2019 from 11:00 to 12:00 (Europe/Amsterdam / UTC200)
  • Where Room L016 CWI
  • Contact Name
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Iedereen is welkom om de N & O-lezing van Lucas Slot bij te wonen met de titel: Verbeterde convergentie-analyse van de op maatregelen gebaseerde bovengrenzen van Lasserre voor polynomiale minimalisatie op compacte sets.

We investigate the convergence rate of a hierarchy of measure-based upper bounds introduced by Lasserre (2011) for the minimization of a polynomial f over a compact set K.
These bounds are obtained by searching for a degree 2r sum-of-squares density function h minimizing the expected value of f over K with respect to some fixed reference measure supported on K.
The convergence rate of these bounds to the global minimum of f over K is known to be in O(1/r^2) when K is the box, equipped with the Chebyshev measure. We extend this error estimate to a wider class of convex bodies, while also allowing for a broader class of reference measures, including the Lebesgue measure. Our analysis applies to simplices, balls and convex bodies that locally look like a ball.
Bovendien tonen we een convergentiesnelheid in O ((log r) / r) wanneer K voldoet aan een kleine geometrische conditie en een snelheid in O (((log r) / r) ^ 2) wanneer K
een convex lichaam is, dat verbetert op de momenteel bekendste grenzen voor deze gevallen in respectievelijk O (1 / sqrt (r)) en O (1 / r).
Gezamenlijk werk met Monique Laurent.