HEC Montréal, Canada, 6 - 8 mai 2013

Journées de l'optimisation 2013

HEC Montréal, Canada, 6 — 8 mai 2013

Horaire Auteurs Mon horaire

WAP Séance plénière V / Plenary Session V

8 mai 2013 09h00 – 10h00

Salle: Amphithéâtre IBM

Présidée par Dominique Orban

1 présentation

  • 09h00 - 09h25

    Fast Fourier Optimization: High-Contrast Imaging and the Search for Exoplanets

    • Robert J. Vanderbei, prés., Princeton University

    Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the fast Fourier transform (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the “fast Fourier” version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is often a good thing.