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Gradient regularization of Newton method with Bregman distances

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Main Authors: Nikita, Doikov, Yurii, Nesterov
Format: Book
Language:English
Published: Springer 2023
Subjects:
order O(k−2) both
Lipschitz continuity of its Hessian
Online Access:https://link.springer.com/article/10.1007/s10107-023-01943-7
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7538
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spelling 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 Digital Phenikaa
collection Digital Phenikaa
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
_version_ 1762365500027830272
score 8.891145

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