Nonlinear and degenerate discounted approximation in discrete weak KAM theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916150415196160 |
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| author | Ni, Panrui Zavidovique, Maxime |
| author_facet | Ni, Panrui Zavidovique, Maxime |
| contents | In this paper, we introduce a discrete version of the nonlinear implicit Lax-Oleinik operator. We consider the associated vanishing discount problem with a non-degenerate condition and prove convergence of solutions as the discount factor goes to $0$. We also discuss the uniqueness of the discounted solution. The convergence result is a selection principle for fixed points of a family of nonlinear operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear and degenerate discounted approximation in discrete weak KAM theory Ni, Panrui Zavidovique, Maxime Optimization and Control In this paper, we introduce a discrete version of the nonlinear implicit Lax-Oleinik operator. We consider the associated vanishing discount problem with a non-degenerate condition and prove convergence of solutions as the discount factor goes to $0$. We also discuss the uniqueness of the discounted solution. The convergence result is a selection principle for fixed points of a family of nonlinear operators. |
| title | Nonlinear and degenerate discounted approximation in discrete weak KAM theory |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.04563 |