4.6 Article

A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization

Journal

INVERSE PROBLEMS
Volume 37, Issue 7, Pages -

Publisher

IOP Publishing Ltd
DOI: 10.1088/1361-6420/ac0966

Keywords

non-convex optimization; stochastic ADMM; variance reduction stochastic gradient

Funding

  1. National key research and development program [2017YFB0202902]
  2. National Natural Science Foundation of China [11771288, 12090024]
  3. Leverhulme Trust
  4. Newton Trust

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The paper proposes combining ADMM with a class of variance-reduced stochastic gradient estimators for solving large-scale non-convex and non-smooth optimization problems. Global convergence is established under the additional assumption that the object function satisfies Kurdyka-Lojasiewicz property, and numerical experiments are conducted to demonstrate the performance of the proposed methods.
Alternating direction method of multipliers (ADMM) is a popular first-order method owing to its simplicity and efficiency. However, similar to other proximal splitting methods, the performance of ADMM degrades significantly when the scale of optimization problems to solve becomes large. In this paper, we consider combining ADMM with a class of variance-reduced stochastic gradient estimators for solving large-scale non-convex and non-smooth optimization problems. Global convergence of the generated sequence is established under the additional assumption that the object function satisfies Kurdyka-Lojasiewicz property. Numerical experiments on graph-guided fused lasso and computed tomography are presented to demonstrate the performance of the proposed methods.

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