Set-valued Hamilton-Jacobi-Bellman Equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913993432498176 |
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| author | İşeri, Melih Zhang, Jianfeng |
| author_facet | İşeri, Melih Zhang, Jianfeng |
| contents | Building upon the dynamic programming principle for set-valued functions arising from many applications, in this paper we propose a new notion of set-valued PDEs. The key component in the theory is a set-valued Itô formula, characterizing the flows on the surface of the dynamic sets. In the contexts of multivariate control problems, we establish the wellposedness of the set-valued HJB equations, which extends the standard HJB equations in the scalar case to the multivariate case. As an application, a moving scalarization for certain time inconsistent problems is constructed by using the classical solution of the set-valued HJB equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Set-valued Hamilton-Jacobi-Bellman Equations İşeri, Melih Zhang, Jianfeng Optimization and Control 49L12 (Primary) 49J53, 60H30, 49J20, 47H04 (Secondary) Building upon the dynamic programming principle for set-valued functions arising from many applications, in this paper we propose a new notion of set-valued PDEs. The key component in the theory is a set-valued Itô formula, characterizing the flows on the surface of the dynamic sets. In the contexts of multivariate control problems, we establish the wellposedness of the set-valued HJB equations, which extends the standard HJB equations in the scalar case to the multivariate case. As an application, a moving scalarization for certain time inconsistent problems is constructed by using the classical solution of the set-valued HJB equation. |
| title | Set-valued Hamilton-Jacobi-Bellman Equations |
| topic | Optimization and Control 49L12 (Primary) 49J53, 60H30, 49J20, 47H04 (Secondary) |
| url | https://arxiv.org/abs/2311.05727 |