A New Exact Worst-Case Linear Convergence Rate of the Proximal Gradient Method

Xiaoya Zhang; Hui Zhang

A New Exact Worst-Case Linear Convergence Rate of the Proximal Gradient Method

Optimization and Control 2019-03-13 v2

Authors: Xiaoya Zhang , Hui Zhang

Abstract

In this note, we establish a new exact worst-case linear convergence rate of the proximal gradient method in terms of the proximal gradient norm, which complements the recent results in [1] and implies a refined descent lemma.descent lemma. Based on the new lemma, we improve the linear convergence rate of the objective function accuracy under the Polyak-Lojasiewicz inequality.

Keywords

gradient descent optimization proximal optimization stochastic optimization

Cite

@article{arxiv.1902.09181,
  title  = {A New Exact Worst-Case Linear Convergence Rate of the Proximal Gradient Method},
  author = {Xiaoya Zhang and Hui Zhang},
  journal= {arXiv preprint arXiv:1902.09181},
  year   = {2019}
}

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