separable convex optimization

A Modified Proximal Symmetric ADMM for Multi-Block Separable Convex Optimization with Linear Constraints

  • Yuan Shen
  • Xiayang Zhang
  • Yannian Zuo
    • Categories Convex Optimization Tags , , ,

    We consider the linearly constrained separable convex optimization problem whose objective function is separable w.r.t. $m$ blocks of variables. A bunch of methods have been proposed and well studied. Specifically, a modified strictly contractive Peaceman-Rachford splitting method (SC-PRCM) has been well studied in the literature for the special case of $m=3$. Based on the modified … Read more

    A Partial PPa S-ADMM for Multi-Block for Separable Convex Optimization with Linear Constraints

  • Yuan Shen
  • Aolin Yu
  • Yannian Zuo
    • Categories Convex Optimization Tags , , , ,

    The symmetric alternating direction method of multipliers (S-ADMM) is a classical effective method for solving two-block separable convex optimization. However, its convergence may not be guaranteed for multi-block case providing there is no additional assumptions. In this paper, we propose a partial PPa S-ADMM (referred as P3SADMM), which updates the Lagrange multiplier twice with suitable … Read more

    AN INEXACT PERTURBED PATH-FOLLOWING METHOD FOR LAGRANGIAN DECOMPOSITION IN LARGE-SCALE SEPARABLE CONVEX OPTIMIZATION

  • Moritz Diehl
  • Ion Necoara
  • Carlo Savorgnan
  • Quoc Tran-Dinh
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Parallel Algorithms Tags , , , , ,

    This paper studies an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale separable convex programming problems. Unlike the exact versions considered in the literature, we propose to solve the primal subproblems inexactly up to a given accuracy. This leads to an inexactness of the gradient vector and the Hessian … Read more

    An interior-point Lagrangian decomposition method for separable convex optimization

  • Ion Necoara
  • Johan Suykens
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , ,

    In this paper we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newton … Read more