Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization
Author
Abstract
Suggested Citation
DOI: 10.1007/s10589-021-00286-3
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Filip Hanzely & Peter Richtárik & Lin Xiao, 2021. "Accelerated Bregman proximal gradient methods for relatively smooth convex optimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 405-440, June.
- Haihao Lu & Robert M. Freund & Yurii Nesterov, 2018. "Relatively smooth convex optimization by first-order methods, and applications," LIDAM Reprints CORE 2965, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
- Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
- Masoud Ahookhosh, 2019. "Accelerated first-order methods for large-scale convex optimization: nearly optimal complexity under strong convexity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 319-353, June.
- NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Yurii Nesterov, 2018. "Smooth Convex Optimization," Springer Optimization and Its Applications, in: Lectures on Convex Optimization, edition 2, chapter 0, pages 59-137, Springer.
- P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
- POMPILI, Filippo & GILLIS, Nicolas & ABSIL, Pierre-Antoine & GLINEUR, François, 2014. "Two algorithms for orthogonal nonnegative matrix factorization with application to clusterin," LIDAM Reprints CORE 2581, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Radu Ioan Bot & Dang-Khoa Nguyen, 2020. "The Proximal Alternating Direction Method of Multipliers in the Nonconvex Setting: Convergence Analysis and Rates," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 682-712, May.
- Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.
- Heinz H. Bauschke & Jérôme Bolte & Marc Teboulle, 2017. "A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 330-348, May.
- Heinz H. Bauschke & Jérôme Bolte & Jiawei Chen & Marc Teboulle & Xianfu Wang, 2019. "On Linear Convergence of Non-Euclidean Gradient Methods without Strong Convexity and Lipschitz Gradient Continuity," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1068-1087, September.
- Ron Shefi & Marc Teboulle, 2016. "On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(1), pages 27-46, February.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Xue Gao & Xingju Cai & Xiangfeng Wang & Deren Han, 2023. "An alternating structure-adapted Bregman proximal gradient descent algorithm for constrained nonconvex nonsmooth optimization problems and its inertial variant," Journal of Global Optimization, Springer, vol. 87(1), pages 277-300, September.
- Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.
- Emanuel Laude & Peter Ochs & Daniel Cremers, 2020. "Bregman Proximal Mappings and Bregman–Moreau Envelopes Under Relative Prox-Regularity," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 724-761, March.
- Yin Liu & Sam Davanloo Tajbakhsh, 2023. "Stochastic Composition Optimization of Functions Without Lipschitz Continuous Gradient," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 239-289, July.
- Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
- Masoud Ahookhosh, 2019. "Accelerated first-order methods for large-scale convex optimization: nearly optimal complexity under strong convexity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 319-353, June.
- Xue Gao & Xingju Cai & Xiangfeng Wang & Deren Han, 2023. "An alternating structure-adapted Bregman proximal gradient descent algorithm for constrained nonconvex nonsmooth optimization problems and its inertial variant," Journal of Global Optimization, Springer, vol. 87(1), pages 277-300, September.
- Abbaszadehpeivasti, Hadi, 2024. "Performance analysis of optimization methods for machine learning," Other publications TiSEM 3050a62d-1a1f-494e-99ef-7, Tilburg University, School of Economics and Management.
- Zhongming Wu & Chongshou Li & Min Li & Andrew Lim, 2021. "Inertial proximal gradient methods with Bregman regularization for a class of nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 79(3), pages 617-644, March.
- Filip Hanzely & Peter Richtárik & Lin Xiao, 2021. "Accelerated Bregman proximal gradient methods for relatively smooth convex optimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 405-440, June.
- Dewei Zhang & Yin Liu & Sam Davanloo Tajbakhsh, 2022. "A First-Order Optimization Algorithm for Statistical Learning with Hierarchical Sparsity Structure," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1126-1140, March.
- S. Bonettini & M. Prato & S. Rebegoldi, 2018. "A block coordinate variable metric linesearch based proximal gradient method," Computational Optimization and Applications, Springer, vol. 71(1), pages 5-52, September.
- Radu-Alexandru Dragomir & Alexandre d’Aspremont & Jérôme Bolte, 2021. "Quartic First-Order Methods for Low-Rank Minimization," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 341-363, May.
- Yaohua Hu & Chong Li & Kaiwen Meng & Xiaoqi Yang, 2021. "Linear convergence of inexact descent method and inexact proximal gradient algorithms for lower-order regularization problems," Journal of Global Optimization, Springer, vol. 79(4), pages 853-883, April.
- Zhigang Li & Mingchuan Zhang & Junlong Zhu & Ruijuan Zheng & Qikun Zhang & Qingtao Wu, 2018. "Stochastic Block-Coordinate Gradient Projection Algorithms for Submodular Maximization," Complexity, Hindawi, vol. 2018, pages 1-11, December.
- Vincenzo Bonifaci, 2021. "A Laplacian approach to $$\ell _1$$ ℓ 1 -norm minimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 441-469, June.
- Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
- Doikov, Nikita & Nesterov, Yurii, 2020. "Affine-invariant contracting-point methods for Convex Optimization," LIDAM Discussion Papers CORE 2020029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Quoc Tran-Dinh, 2019. "Proximal alternating penalty algorithms for nonsmooth constrained convex optimization," Computational Optimization and Applications, Springer, vol. 72(1), pages 1-43, January.
- Yangyang Xu, 2019. "Asynchronous parallel primal–dual block coordinate update methods for affinely constrained convex programs," Computational Optimization and Applications, Springer, vol. 72(1), pages 87-113, January.
- Mingyi Hong & Tsung-Hui Chang & Xiangfeng Wang & Meisam Razaviyayn & Shiqian Ma & Zhi-Quan Luo, 2020. "A Block Successive Upper-Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 833-861, August.
More about this item
Keywords
Nonsmooth nonconvex optimization; Proximal alternating linearized minimization; Bregman distance; Multi-block relative smoothness; KL inequality; Orthogonal nonnegative matrix factorization;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:79:y:2021:i:3:d:10.1007_s10589-021-00286-3. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.