Generalized Mirror Prox Algorithm for Monotone Variational Inequalities: Universality and Inexact Oracle
Author
Abstract
Suggested Citation
DOI: 10.1007/s10957-022-02062-7
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
- Pavel Dvurechensky & Yurii Nesterov & Vladimir Spokoiny, 2015. "Primal-Dual Methods for Solving Infinite-Dimensional Games," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 23-51, July.
- DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011.
"First-order methods of smooth convex optimization with inexact oracle,"
LIDAM Discussion Papers CORE
2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2014. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Reprints CORE 2594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- NESTEROV, Yurii, 2015. "Universal gradient methods for convex optimization problems," LIDAM Reprints CORE 2701, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Dvurechensky, Pavel & Gorbunov, Eduard & Gasnikov, Alexander, 2021. "An accelerated directional derivative method for smooth stochastic convex optimization," European Journal of Operational Research, Elsevier, vol. 290(2), pages 601-621.
- Pham Khanh & Phan Vuong, 2014. "Modified projection method for strongly pseudomonotone variational inequalities," Journal of Global Optimization, Springer, vol. 58(2), pages 341-350, February.
- NESTEROV, Yu, 2003. "Dual extrapolation and its applications for solving variational inequalities and related problems," LIDAM Discussion Papers CORE 2003068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- DVURECHENSKY, Pavel & NESTEROV, Yurii & SPOKOINY, Vladimir, 2015. "Primal-dual methods for solving infinite-dimensional games," LIDAM Reprints CORE 2700, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Cong Dang & Guanghui Lan, 2015. "On the convergence properties of non-Euclidean extragradient methods for variational inequalities with generalized monotone operators," Computational Optimization and Applications, Springer, vol. 60(2), pages 277-310, March.
- NESTEROV, Yurii & SCRIMALI, Laura, 2011. "Solving strongly monotone variational and quasi-variational inequalities," LIDAM Reprints CORE 2357, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Pavel Dvurechensky & Alexander Gasnikov, 2016. "Stochastic Intermediate Gradient Method for Convex Problems with Stochastic Inexact Oracle," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 121-145, October.
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.- Masaru Ito, 2016. "New results on subgradient methods for strongly convex optimization problems with a unified analysis," Computational Optimization and Applications, Springer, vol. 65(1), pages 127-172, September.
- Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
- Fedor Stonyakin & Ilya Kuruzov & Boris Polyak, 2023. "Stopping Rules for Gradient Methods for Non-convex Problems with Additive Noise in Gradient," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 531-551, August.
- Bruce Cox & Anatoli Juditsky & Arkadi Nemirovski, 2017. "Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 402-435, February.
- Masoud Ahookhosh & Arnold Neumaier, 2018. "Solving structured nonsmooth convex optimization with complexity $$\mathcal {O}(\varepsilon ^{-1/2})$$ O ( ε - 1 / 2 )," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 110-145, April.
- 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.
- Tianxiao Sun & Ion Necoara & Quoc Tran-Dinh, 2020. "Composite convex optimization with global and local inexact oracles," Computational Optimization and Applications, Springer, vol. 76(1), pages 69-124, May.
- Dvurechensky, Pavel & Gorbunov, Eduard & Gasnikov, Alexander, 2021. "An accelerated directional derivative method for smooth stochastic convex optimization," European Journal of Operational Research, Elsevier, vol. 290(2), pages 601-621.
- Vladimir Krutikov & Svetlana Gutova & Elena Tovbis & Lev Kazakovtsev & Eugene Semenkin, 2022. "Relaxation Subgradient Algorithms with Machine Learning Procedures," Mathematics, MDPI, vol. 10(21), pages 1-33, October.
- Elena Tovbis & Vladimir Krutikov & Predrag Stanimirović & Vladimir Meshechkin & Aleksey Popov & Lev Kazakovtsev, 2023. "A Family of Multi-Step Subgradient Minimization Methods," Mathematics, MDPI, vol. 11(10), pages 1-24, May.
- TAYLOR, Adrien B. & HENDRICKX, Julien M. & François GLINEUR, 2016.
"Exact worst-case performance of first-order methods for composite convex optimization,"
LIDAM Discussion Papers CORE
2016052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Adrien B. TAYLOR & Julien M. HENDRICKX & François GLINEUR, 2017. "Exact worst-case performance of first-order methods for composite convex optimization," LIDAM Reprints CORE 2875, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Xuexue Zhang & Sanyang Liu & Nannan Zhao, 2023. "An Extended Gradient Method for Smooth and Strongly Convex Functions," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
- Dang Hieu & Pham Ky Anh & Le Dung Muu, 2019. "Modified extragradient-like algorithms with new stepsizes for variational inequalities," Computational Optimization and Applications, Springer, vol. 73(3), pages 913-932, July.
- Xiao-Juan Zhang & Xue-Wu Du & Zhen-Ping Yang & Gui-Hua Lin, 2019. "An Infeasible Stochastic Approximation and Projection Algorithm for Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1053-1076, December.
- Trinh Ngoc Hai, 2020. "Two modified extragradient algorithms for solving variational inequalities," Journal of Global Optimization, Springer, vol. 78(1), pages 91-106, September.
- DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2013. "First-order methods with inexact oracle: the strongly convex case," LIDAM Discussion Papers CORE 2013016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- NESTEROV, Yu., 2005. "Minimizing functions with bounded variation of subgradients," LIDAM Discussion Papers CORE 2005079, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Le Thi Khanh Hien & Cuong V. Nguyen & Huan Xu & Canyi Lu & Jiashi Feng, 2019. "Accelerated Randomized Mirror Descent Algorithms for Composite Non-strongly Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 541-566, May.
- DEVOLDER, Olivier, 2011. "Stochastic first order methods in smooth convex optimization," LIDAM Discussion Papers CORE 2011070, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
More about this item
Keywords
Variational inequality; monotone operator; Hölder continuity; Inexact oracle; Complexity estimate;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:194:y:2022:i:3:d:10.1007_s10957-022-02062-7. 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.