indefinite proximal term

A faster proximal-indefinite augmented Lagrangian method with O(1/k^2 ) convergence rate

  • Jianchao Bai
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    The Augmented Lagrangian Method (ALM), firstly proposed in 1969, remains a vital framework in large-scale constrained optimization. This paper addresses a linearly constrained composite convex minimization problem and presents a general proximal ALM that incorporates both Nesterov acceleration and relaxed acceleration, while enjoying a proximal-indefinite term. Under mild assumptions (potentially without requiring prior knowledge of … Read more

    An inexact ADMM with proximal-indefinite term and larger stepsize

  • Yuxue Ma
  • Jianchao Bai
    • Categories Convex Optimization Tags , , , ,

    In this paper, an inexact Alternating Direction Method of Multipliers (ADMM) has been proposed for solving the two-block separable convex optimization problem subject to linear equality constraints. The first resulting subproblem is solved inexactly under relative error criterion, while another subproblem called regularization problem is solved inexactly by introducing an indefinite proximal term. Meanwhile, the … Read more

    Accelerated Stochastic Peaceman-Rachford Method for Empirical Risk Minimization

  • Jianchao Bai
  • Fengmiao Bian
  • Xiaokai Chang
  • Lin Du
    • Categories Convex Optimization, Stochastic Programming Tags , , , ,

    This work is devoted to studying an Accelerated Stochastic Peaceman-Rachford Splitting Method (AS-PRSM) for solving a family of structural empirical risk minimization problems. The objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite-sum of smooth convex component functions. The smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction … Read more