Отправить статью по E-mail An Adaptive Proximal Method for Variational Inequalities
- Авторы: Gasnikov A.V.1,2,3, Dvurechensky P.E.3,4, Stonyakin F.S.5,1, Titov A.A.1
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Учреждения:
- Moscow Institute of Physics and Technology
- State University—Higher School of Economics
- Kharkevich Institute for Information Transmission Problems
- Weierstrass Institute for Applied Analysis and Stochastics
- Crimea Federal University
- Выпуск: Том 59, № 5 (2019)
- Страницы: 836-841
- Раздел: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180593
- DOI: https://doi.org/10.1134/S0965542519050075
- ID: 180593
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Аннотация
A novel analog of Nemirovski’s proximal mirror method with an adaptive choice of constants in the minimized prox-mappings at each iteration for variational inequalities with a Lipschitz continuous field is proposed. Estimates of the number of iterations needed to attain the desired quality of solution of the variational inequality are obtained. It is shown how the proposed approach can be extended for the case of Hölder continuous field. A modification of the proposed algorithm for the case of an inexact oracle for the field operator is also considered.
Об авторах
A. Gasnikov
Moscow Institute of Physics and Technology; State University—Higher School of Economics; Kharkevich Institute for Information Transmission Problems
Автор, ответственный за переписку.
Email: gasnikov@yandex.ru
Россия, Dolgoprudnyi, Moscow oblast, 141700; Moscow, 125319; Moscow, 127051
P. Dvurechensky
Kharkevich Institute for Information Transmission Problems; Weierstrass Institute for Applied Analysis and Stochastics
Автор, ответственный за переписку.
Email: pavel.dvurechensky@gmail.com
Россия, Moscow, 127051; Berlin, 10117
F. Stonyakin
Crimea Federal University; Moscow Institute of Physics and Technology
Автор, ответственный за переписку.
Email: fedyor@mail.ru
Россия, Simferopol, 295007; Dolgoprudnyi, Moscow oblast, 141700
A. Titov
Moscow Institute of Physics and Technology
Автор, ответственный за переписку.
Email: a.a.titov@phystech.edu
Россия, Dolgoprudnyi, Moscow oblast, 141700
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