Optimal bounds for numerical approximations of finite horizon problems based on dynamic programming approach
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908839898513408 |
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| author | de Frutos, Javier Novo, Julia |
| author_facet | de Frutos, Javier Novo, Julia |
| contents | In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the
finite horizon case. We prove an a priori bound of size $O(h+k)$ for the method, $h$ being the time discretization step and $k$ the spatial mesh size. Arguing with piecewise constants controls we are able to obtain first order of convergence in time and space under standard regularity assumptions, avoiding the more restrictive regularity assumptions on the controls required in \cite{nos}.
We show that the loss in the rate of convergence in time of the
infinite case (obtained arguing with piece-wise controls)
can be avoided in the finite horizon case |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal bounds for numerical approximations of finite horizon problems based on dynamic programming approach de Frutos, Javier Novo, Julia Optimization and Control In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a priori bound of size $O(h+k)$ for the method, $h$ being the time discretization step and $k$ the spatial mesh size. Arguing with piecewise constants controls we are able to obtain first order of convergence in time and space under standard regularity assumptions, avoiding the more restrictive regularity assumptions on the controls required in \cite{nos}. We show that the loss in the rate of convergence in time of the infinite case (obtained arguing with piece-wise controls) can be avoided in the finite horizon case |
| title | Optimal bounds for numerical approximations of finite horizon problems based on dynamic programming approach |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.16574 |