first-order primal-dual algorithm

Some Primal-Dual Theory for Subgradient Methods for Strongly Convex Optimization

  • Benjamin Grimmer
  • Danlin Li
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the proximal subgradient method, and the switching subgradient method. These equivalences enable $O(1/T)$ convergence guarantees in terms of both their classic primal gap and a … Read more

    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