Second-order optimality conditions and stability for optimal control problems governed by viscous Camassa-Holm equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912049674584064 |
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| author | Anh, Cung The Giang, Nguyen Hai Ha |
| author_facet | Anh, Cung The Giang, Nguyen Hai Ha |
| contents | This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form were proved for a distributed optimal control problem governed by the three-dimensional viscous Camassa-Holm equations in bounded domains with the cost functional of a quite general form and pointwise control constraints. We will establish the second-order sufficient optimality conditions as well as the Lipschitz stability results of the control system with respect to perturbations of the initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second-order optimality conditions and stability for optimal control problems governed by viscous Camassa-Holm equations Anh, Cung The Giang, Nguyen Hai Ha Optimization and Control This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form were proved for a distributed optimal control problem governed by the three-dimensional viscous Camassa-Holm equations in bounded domains with the cost functional of a quite general form and pointwise control constraints. We will establish the second-order sufficient optimality conditions as well as the Lipschitz stability results of the control system with respect to perturbations of the initial data. |
| title | Second-order optimality conditions and stability for optimal control problems governed by viscous Camassa-Holm equations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.19347 |