A stochastic proximal alternating method for non-smooth non-convex optimization

Derek Driggs, Junqi Tang, Jingwei Liang, Mike Davies, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

In this work, we introduce a novel stochastic proximal alternating linearized minimization algorithm [J. Bolte, S. Sabach, and M. Teboulle, Math. Program., 146 (2014), pp. 459-494] for solving a class of nonsmooth and nonconvex optimization problems. Large-scale imaging problems are becoming
increasingly prevalent due to the advances in data acquisition and computational capabilities. Motivated by the success of stochastic optimization methods, we propose a stochastic variant of proximal alternating linearized minimization. We provide global convergence guarantees, demonstrating that our proposed method with variance-reduced stochastic gradient estimators, such as SAGA [A. Defazio, F. Bach, and S. Lacoste-Julien, Advances in Neural Information Processing Systems, 2014, 15 pp. 1646-1654] and SARAH [L. M. Nguyen, J. Liu, K. Scheinberg, and M. Tak\a\c, Proceedings of the 34th International Conference on Machine Learning, PMLR 70, 2017, pp. 2613-2621], achieves state-of-the-art oracle complexities. We also demonstrate the efficacy of our algorithm via several numerical examples including sparse nonnegative matrix factorization, sparse principal component analysis, and blind image-deconvolution.
Original languageUndefined/Unknown
Pages (from-to)1932–1970
Number of pages39
JournalSiam journal on imaging sciences
Issue number4
Early online date21 Dec 2021
Publication statusE-pub ahead of print - 21 Dec 2021

Keywords / Materials (for Non-textual outputs)

  • math.OC
  • 90C26

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