Subgradient evolution of value functions in discrete-time optimal control
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916111972302848 |
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| author | Deride, Julio Hermosilla, Cristopher Solla, Mattia |
| author_facet | Deride, Julio Hermosilla, Cristopher Solla, Mattia |
| contents | In this paper we investigate how the subgradients of the value function of a discrete-time convex Bolza problem evolve over time. In particular, we develop a discrete-time version of the characteristic method introduced by Rockafellar and Wolenski in the 2000s, by showing that the time-evolution of the subgradients of the value functions can be associated with trajectories of a discrete-time Hamiltonian system. To do so, we first prove that the value function has a dual counterpart, which corresponds to the conjugate of the value function of a suitable dual problem. We finally make a discussion about the qualification conditions we require for our results, showing in particular that classical problems, such as the Liner-Quadratic regulator, satisfy these hypotheses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subgradient evolution of value functions in discrete-time optimal control Deride, Julio Hermosilla, Cristopher Solla, Mattia Optimization and Control 93C55, 46N10, 49N10, 49N15 In this paper we investigate how the subgradients of the value function of a discrete-time convex Bolza problem evolve over time. In particular, we develop a discrete-time version of the characteristic method introduced by Rockafellar and Wolenski in the 2000s, by showing that the time-evolution of the subgradients of the value functions can be associated with trajectories of a discrete-time Hamiltonian system. To do so, we first prove that the value function has a dual counterpart, which corresponds to the conjugate of the value function of a suitable dual problem. We finally make a discussion about the qualification conditions we require for our results, showing in particular that classical problems, such as the Liner-Quadratic regulator, satisfy these hypotheses. |
| title | Subgradient evolution of value functions in discrete-time optimal control |
| topic | Optimization and Control 93C55, 46N10, 49N10, 49N15 |
| url | https://arxiv.org/abs/2402.00289 |