proximal

Analysis and Implementation of an Asynchronous Optimization Algorithm for the Parameter Server

  • Arda Aytekin
  • Hamid Reza Feyzmahdavian
  • Mikael Johansson
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Parallel Algorithms Tags , , , ,

    This paper presents an asynchronous incremental aggregated gradient algorithm and its implementation in a parameter server framework for solving regularized optimization problems. The algorithm can handle both general convex (possibly non-smooth) regularizers and general convex constraints. When the empirical data loss is strongly convex, we establish linear convergence rate, give explicit expressions for step-size choices … Read more

    An inexact block-decomposition method for extra large-scale conic semidefinite programming

  • Renato D.C. Monteiro
  • Camilo Ortiz
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , , , , ,

    In this paper, we present an inexact block-decomposition (BD) first-order method for solving standard form conic semidefinite programming (SDP) which avoids computations of exact projections onto the manifold defined by the affine constraints and, as a result, is able to handle extra large SDP instances. The method is based on a two-block reformulation of the … Read more

    A first-order block-decomposition method for solving two-easy-block structured semidefinite programs

  • Renato D.C. Monteiro
  • Camilo Ortiz
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , , , , , ,

    In this paper, we consider a first-order block-decomposition method for minimizing the sum of a convex differentiable function with Lipschitz continuous gradient, and two other proper closed convex (possibly, nonsmooth) functions with easily computable resolvents. The method presented contains two important ingredients from a computational point of view, namely: an adaptive choice of stepsize for … Read more

    Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems

  • Renato D.C. Monteiro
  • Camilo Ortiz
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , , ,

    In this paper, we consider block-decomposition first-order methods for solving large-scale conic semidefinite programming problems. Several ingredients are introduced to speed-up the method in its pure form such as: an aggressive choice of stepsize for performing the extragradient step; use of scaled inner products in the primal and dual spaces; dynamic update of the scaled … Read more