Laurent Condat

SEMINAIRE DU 7 mai 2015 – 15H @ LTCI – Amphi Saphir

Primal-dual forward-backward splitting for large-scale convex optimization

A wide array of estimation and restoration problems, in particular inverse imaging problems, can be formulated as large-scale convex optimization problems in Hilbert spaces: the goal is to minimize a sum of convex functions, possibly composed with linear operators. The forward-backward splitting technique, when applied in primal-dual product spaces, is a powerful umbrella that encompasses the classical forward-backward, Douglas-Rachford, and Chambolle-Pock algorithms. A useful extension with variable metric is discussed. Some applications in imaging are shown.

Slides  [pdf]

The Speaker

Laurent Condat is a permanent CNRS researcher at GIPSA-lab (Grenoble, France).

Related material

  • L. Condat, “A Generic Proximal Algorithm for Convex Optimization – Application to Total Variation Minimization,” IEEE Signal Proc. Letters, vol. 21, no. 8, pp. 1054-1057, Aug. 2014.  PDF.  Matlab files:
  • L. Condat, “A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms,” J. Optimization Theory and Applications, vol. 158, no. 2, pp. 460-479, 2013.  PDF
  • L. Condat, “A direct algorithm for 1D total variation denoising,” IEEE Signal Proc. Letters, vol. 20, no. 11, pp. 1054-1057, Nov. 2013.  PDF.  C file:  condat_fast_tv.c