Gradient regularization of Newton method with Bregman distances
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| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s10107-023-01943-7 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7538 |
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oai:localhost:PNK-75382023-04-05T03:12:48Z Gradient regularization of Newton method with Bregman distances Nikita, Doikov Yurii, Nesterov order O(k−2) both Lipschitz continuity of its Hessian CC BY In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to the square root of the norm of the current gradient. For the basic scheme, as applied to the composite convex optimization problem, we establish the global convergence rate of the order O(k−2) both in terms of the functional residual and in the norm of subgradients. Our main assumption on the smooth part of the objective is Lipschitz continuity of its Hessian. 2023-04-05T03:12:47Z 2023-04-05T03:12:47Z 2023 Book https://link.springer.com/article/10.1007/s10107-023-01943-7 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7538 en application/pdf Springer |
| institution |
Trường Đại học Phenikaa |
| collection |
DSpace |
| language |
English |
| topic |
order O(k−2) both Lipschitz continuity of its Hessian |
| spellingShingle |
order O(k−2) both Lipschitz continuity of its Hessian Nikita, Doikov Yurii, Nesterov Gradient regularization of Newton method with Bregman distances |
| description |
CC BY |
| format |
Book |
| author |
Nikita, Doikov Yurii, Nesterov |
| author_facet |
Nikita, Doikov Yurii, Nesterov |
| author_sort |
Nikita, Doikov |
| title |
Gradient regularization of Newton method with Bregman distances |
| title_short |
Gradient regularization of Newton method with Bregman distances |
| title_full |
Gradient regularization of Newton method with Bregman distances |
| title_fullStr |
Gradient regularization of Newton method with Bregman distances |
| title_full_unstemmed |
Gradient regularization of Newton method with Bregman distances |
| title_sort |
gradient regularization of newton method with bregman distances |
| publisher |
Springer |
| publishDate |
2023 |
| url |
https://link.springer.com/article/10.1007/s10107-023-01943-7 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7538 |
| work_keys_str_mv |
AT nikitadoikov gradientregularizationofnewtonmethodwithbregmandistances AT yuriinesterov gradientregularizationofnewtonmethodwithbregmandistances |
| _version_ |
1787740805130092544 |