Mathematical and Numerical Analysis to Shrinking-Dimer Saddle Dynamics with Local Lipschitz Conditions Article Swipe
Lei Zhang
,
Pingwen Zhang
,
Xiangcheng Zheng
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.4208/csiam-am.so-2022-0010
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.4208/csiam-am.so-2022-0010
We present a mathematical and numerical investigation to the shrinkingdimer saddle dynamics for finding any-index saddle points in the solution landscape.Due to the dimer approximation of Hessian in saddle dynamics, the local Lipschitz assumptions and the strong nonlinearity for the saddle dynamics, it remains challenges for delicate analysis, such as the boundedness of the solutions and the dimer error.We address these issues to bound the solutions under proper relaxation parameters, based on which we prove the error estimates for numerical discretization to the shrinkingdimer saddle dynamics by matching the dimer length and the time step size.Furthermore, the Richardson extrapolation is employed to obtain a high-order approximation.The inherent reason of requiring the matching of the dimer length and the time step size lies in that the former serves a different mesh size from the later, and thus the proposed numerical method is close to a fully-discrete numerical scheme of some space-time PDE model with the Hessian in the saddle dynamics and its dimer approximation serving as a "spatial operator" and its discretization, respectively, which in turn indicates the PDE nature of the saddle dynamics.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.4208/csiam-am.so-2022-0010
- https://global-sci.org/intro/article_detail/auth/21338.html
- OA Status
- diamond
- Cited By
- 9
- References
- 36
- Related Works
- 10
- OpenAlex ID
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https://openalex.org/W4313800160Canonical identifier for this work in OpenAlex
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https://doi.org/10.4208/csiam-am.so-2022-0010Digital Object Identifier
- Title
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Mathematical and Numerical Analysis to Shrinking-Dimer Saddle Dynamics with Local Lipschitz ConditionsWork title
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articleOpenAlex work type
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enPrimary language
- Publication year
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2023Year of publication
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2023-01-08Full publication date if available
- Authors
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Lei Zhang, Pingwen Zhang, Xiangcheng ZhengList of authors in order
- Landing page
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https://doi.org/10.4208/csiam-am.so-2022-0010Publisher landing page
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https://global-sci.org/intro/article_detail/auth/21338.htmlDirect link to full text PDF
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diamondOpen access status per OpenAlex
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https://global-sci.org/intro/article_detail/auth/21338.htmlDirect OA link when available
- Concepts
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Hessian matrix, Discretization, Mathematics, Lipschitz continuity, Saddle, Saddle point, Applied mathematics, Mathematical analysis, Matching (statistics), Mathematical optimization, Geometry, StatisticsTop concepts (fields/topics) attached by OpenAlex
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9Total citation count in OpenAlex
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2025: 3, 2024: 3, 2023: 3Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.Lipschitz | 32 |
| abstract_inverted_index.analysis, | 47 |
| abstract_inverted_index.any-index | 14 |
| abstract_inverted_index.different | 128 |
| abstract_inverted_index.dynamics, | 29, 41 |
| abstract_inverted_index.dynamics. | 182 |
| abstract_inverted_index.estimates | 77 |
| abstract_inverted_index.indicates | 175 |
| abstract_inverted_index.numerical | 5, 79, 138, 145 |
| abstract_inverted_index.operator" | 167 |
| abstract_inverted_index.requiring | 109 |
| abstract_inverted_index.solutions | 54, 65 |
| abstract_inverted_index.Richardson | 97 |
| abstract_inverted_index.challenges | 44 |
| abstract_inverted_index.high-order | 104 |
| abstract_inverted_index.relaxation | 68 |
| abstract_inverted_index.space-time | 149 |
| abstract_inverted_index.assumptions | 33 |
| abstract_inverted_index.boundedness | 51 |
| abstract_inverted_index.parameters, | 69 |
| abstract_inverted_index.mathematical | 3 |
| abstract_inverted_index.nonlinearity | 37 |
| abstract_inverted_index.approximation | 24, 162 |
| abstract_inverted_index.extrapolation | 98 |
| abstract_inverted_index.investigation | 6 |
| abstract_inverted_index.landscape.Due | 20 |
| abstract_inverted_index.respectively, | 171 |
| abstract_inverted_index.discretization | 80 |
| abstract_inverted_index.fully-discrete | 144 |
| abstract_inverted_index.shrinkingdimer | 9, 83 |
| abstract_inverted_index.discretization, | 170 |
| abstract_inverted_index.approximation.The | 105 |
| abstract_inverted_index.size.Furthermore, | 95 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 96 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.94498834 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |