On the non-ergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming

Ya-Feng Liu; Xin Liu; Shiqian Ma

On the non-ergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming

Optimization and Control 2018-03-30 v3

Authors: Ya-Feng Liu , Xin Liu , Shiqian Ma

Abstract

In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The stopping criterion used in solving the augmented Lagrangian (AL) subproblem in the proposed IAL framework is weaker and potentially much easier to check than the one used in most of the existing IAL frameworks/methods. We analyze the global convergence and the non-ergodic convergence rate of the proposed IAL framework.

Keywords

composite convex optimization linearly constrained inexact augmented Lagrangian augmented Lagrangian subproblem global convergence non-ergodic convergence rate

Cite

@article{arxiv.1603.05738,
  title  = {On the non-ergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming},
  author = {Ya-Feng Liu and Xin Liu and Shiqian Ma},
  journal= {arXiv preprint arXiv:1603.05738},
  year   = {2018}
}

Comments

accepted in Mathematics of Operations Research. arXiv admin note: text overlap with arXiv:1507.07624

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