Inertial primal-dual dynamics with Hessian-driven damping and Tikhonov regularization for convex-concave bilinear saddle point problems Article Swipe
Xiangkai Sun
,
Liang He
,
Xian-Jun Long
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.05931
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.05931
This paper deals with a second-order primal-dual dynamical system with Hessian-driven damping and Tikhonov regularization terms in connection with a convex-concave bilinear saddle point problem. We first obtain a fast convergence rate of the primal-dual gap along the trajectory generated by the dynamical system, and provide some integral estimates. Then, based on the setting of the parameters involved, we demonstrate that both the convergence rate of the primal-dual gap and the strong convergence of the trajectory can be achieved simultaneously. Furthermore, we evaluate the performance of the proposed system using two numerical examples.
Related Topics
Concepts
Tikhonov regularization
Hessian matrix
Saddle point
Saddle
Bilinear interpolation
Mathematics
Regularization (linguistics)
Regular polygon
Mathematical analysis
Dual (grammatical number)
Inertial frame of reference
Applied mathematics
Mathematical optimization
Physics
Computer science
Inverse problem
Geometry
Classical mechanics
Statistics
Artificial intelligence
Art
Literature
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2412.05931
- https://arxiv.org/pdf/2412.05931
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4405253746
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4405253746Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2412.05931Digital Object Identifier
- Title
-
Inertial primal-dual dynamics with Hessian-driven damping and Tikhonov regularization for convex-concave bilinear saddle point problemsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-12-08Full publication date if available
- Authors
-
Xiangkai Sun, Liang He, Xian-Jun LongList of authors in order
- Landing page
-
https://arxiv.org/abs/2412.05931Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2412.05931Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2412.05931Direct OA link when available
- Concepts
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Tikhonov regularization, Hessian matrix, Saddle point, Saddle, Bilinear interpolation, Mathematics, Regularization (linguistics), Regular polygon, Mathematical analysis, Dual (grammatical number), Inertial frame of reference, Applied mathematics, Mathematical optimization, Physics, Computer science, Inverse problem, Geometry, Classical mechanics, Statistics, Artificial intelligence, Art, LiteratureTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.connection | 17 |
| abstract_inverted_index.estimates. | 48 |
| abstract_inverted_index.parameters | 56 |
| abstract_inverted_index.trajectory | 38, 75 |
| abstract_inverted_index.convergence | 30, 63, 72 |
| abstract_inverted_index.demonstrate | 59 |
| abstract_inverted_index.performance | 84 |
| abstract_inverted_index.primal-dual | 6, 34, 67 |
| abstract_inverted_index.Furthermore, | 80 |
| abstract_inverted_index.second-order | 5 |
| abstract_inverted_index.Hessian-driven | 10 |
| abstract_inverted_index.convex-concave | 20 |
| abstract_inverted_index.regularization | 14 |
| abstract_inverted_index.simultaneously. | 79 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |