Antonin Chambolle

A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions

  • Antonin Chambolle
  • Thomas Pock
    • Categories Convex and Nonsmooth Optimization Tags , ,

    We analyze alternating descent algorithms for minimizing the sum of a quadratic function and block separable non-smooth functions. In case the quadratic interactions between the blocks are pairwise, we show that the schemes can be accelerated, leading to improved convergence rates with respect to related accelerated parallel proximal descent. As an application we obtain very … Read more

    On the ergodic convergence rates of a first-order primal-dual algorithm

  • Antonin Chambolle
  • Thomas Pock
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    We revisit the proofs of convergence for a first order primal-dual algorithm for convex optimization which we have studied a few years ago. In particular, we prove rates of convergence for a more general version, with simpler proofs and more complete results. ArticleDownload View PDF

    A first-order primal-dual algorithm for convex problems with applications to imaging

  • Antonin Chambolle
  • Thomas Pock
    • Categories Convex and Nonsmooth Optimization Tags , ,

    In this paper we study a first-order primal-dual algorithm for convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N ) in finite dimensions, which is optimal for the complete class of non-smooth problems we are considering in this paper. We further show accelerations of the proposed algorithm to … Read more