Continuous and discrete-time accelerated methods for an inequality constrained convex optimization problem Article Swipe
Juan Liu
,
Nan-Jing Huang
,
Xian-Jun Long
,
Xue-song Li
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.14828
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.14828
This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the logarithmic barrier function. Using the Hamiltonian principle, we propose a continuous-time dynamical system associated with a Bregman Lagrangian for solving the unconstrained optimization problem. Under certain conditions, we demonstrate that this continuous-time dynamical system exponentially converges to the optimal solution of the inequality constrained convex optimization problem. Moreover, we derive several discrete-time algorithms from this continuous-time framework and obtain their optimal convergence rates. Finally, we present numerical experiments to validate the effectiveness of the proposed algorithms.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2411.14828
- https://arxiv.org/pdf/2411.14828
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4404987442
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4404987442Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2411.14828Digital Object Identifier
- Title
-
Continuous and discrete-time accelerated methods for an inequality constrained convex optimization problemWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-11-22Full publication date if available
- Authors
-
Juan Liu, Nan-Jing Huang, Xian-Jun Long, Xue-song LiList of authors in order
- Landing page
-
https://arxiv.org/abs/2411.14828Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2411.14828Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2411.14828Direct OA link when available
- Concepts
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Inequality, Mathematical optimization, Convex optimization, Mathematics, Regular polygon, Optimization problem, Linear matrix inequality, Continuous optimization, Discrete time and continuous time, Applied mathematics, Mathematical analysis, Geometry, Statistics, Multi-swarm optimizationTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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