Douglas–Rachford Splitting for the Sum of a Lipschitz Continuous and a Strongly Monotone Operator
Author
Abstract
Suggested Citation
DOI: 10.1007/s10957-019-01517-8
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
- Jingwei Liang & Jalal Fadili & Gabriel Peyré, 2017. "Local Convergence Properties of Douglas–Rachford and Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 874-913, March.
- Regina S. Burachik & Alfredo N. Iusem, 2008. "Set-Valued Mappings and Enlargements of Monotone Operators," Springer Optimization and Its Applications, Springer, number 978-0-387-69757-4, December.
- Regina S. Burachik & Alfredo N. Iusem, 2008. "Enlargements of Monotone Operators," Springer Optimization and Its Applications, in: Set-Valued Mappings and Enlargements of Monotone Operators, chapter 0, pages 161-220, Springer.
- Laurent Condat, 2013. "A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 460-479, August.
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.- Huynh Van Ngai & Nguyen Huu Tron & Michel Théra, 2014. "Metric Regularity of the Sum of Multifunctions and Applications," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 355-390, February.
- Dawan Chumpungam & Panitarn Sarnmeta & Suthep Suantai, 2021. "A New Forward–Backward Algorithm with Line Searchand Inertial Techniques for Convex Minimization Problems with Applications," Mathematics, MDPI, vol. 9(13), pages 1-20, July.
- Sedi Bartz & Minh N. Dao & Hung M. Phan, 2022. "Conical averagedness and convergence analysis of fixed point algorithms," Journal of Global Optimization, Springer, vol. 82(2), pages 351-373, February.
- Bello Cruz, J.Y. & Iusem, A.N., 2015. "Full convergence of an approximate projection method for nonsmooth variational inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 114(C), pages 2-13.
- Regina S. Burachik & Minh N. Dao & Scott B. Lindstrom, 2021. "Generalized Bregman Envelopes and Proximity Operators," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 744-778, September.
- Warunun Inthakon & Suthep Suantai & Panitarn Sarnmeta & Dawan Chumpungam, 2020. "A New Machine Learning Algorithm Based on Optimization Method for Regression and Classification Problems," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
- Juan Pablo Luna & Claudia Sagastizábal & Mikhail Solodov, 2020. "A class of Benders decomposition methods for variational inequalities," Computational Optimization and Applications, Springer, vol. 76(3), pages 935-959, July.
- Heinz H. Bauschke & Warren L. Hare & Walaa M. Moursi, 2016. "On the Range of the Douglas–Rachford Operator," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 884-897, August.
- Hsien-Chung Wu, 2018. "Near Fixed Point Theorems in Hyperspaces," Mathematics, MDPI, vol. 6(6), pages 1-15, May.
- Walaa M. Moursi, 2018. "The Forward–Backward Algorithm and the Normal Problem," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 605-624, March.
- Dawan Chumpungam & Panitarn Sarnmeta & Suthep Suantai, 2022. "An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning," Mathematics, MDPI, vol. 10(9), pages 1-20, April.
- Yunier Bello-Cruz & Guoyin Li & Tran T. A. Nghia, 2021. "On the Linear Convergence of Forward–Backward Splitting Method: Part I—Convergence Analysis," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 378-401, February.
- Regina S. Burachik & Alfredo N. Iusem & Jefferson G. Melo, 2013. "An Inexact Modified Subgradient Algorithm for Primal-Dual Problems via Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 108-131, April.
- L. C. Ceng & B. S. Mordukhovich & J. C. Yao, 2010. "Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 267-303, August.
- J. Bello Cruz & A. Iusem, 2010. "Convergence of direct methods for paramonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 46(2), pages 247-263, June.
- Rubén López, 2013. "Variational convergence for vector-valued functions and its applications to convex multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 1-34, August.
- Jonathan M. Borwein & Liangjin Yao, 2013. "Structure Theory for Maximally Monotone Operators with Points of Continuity," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 1-24, April.
- Ludovic Nagesseur, 2016. "A bundle method using two polyhedral approximations of the $$\varepsilon $$ ε -enlargement of a maximal monotone operator," Computational Optimization and Applications, Springer, vol. 64(1), pages 75-100, May.
- Edvaldo E. A. Batista & Glaydston de Carvalho Bento & Orizon P. Ferreira, 2016. "Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 916-931, September.
- J. Y. Bello Cruz & R. Díaz Millán, 2016. "A relaxed-projection splitting algorithm for variational inequalities in Hilbert spaces," Journal of Global Optimization, Springer, vol. 65(3), pages 597-614, July.
More about this item
Keywords
Douglas–Rachford algorithm; Linear convergence; Lipschitz continuous mapping; Skew-symmetric operator; Strongly convex function; Strongly monotone operator;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:joptap:v:183:y:2019:i:1:d:10.1007_s10957-019-01517-8. 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.