Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912467145195520 |
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| author | Chhatoi, Saroj Prasad Henrion, Didier Marx, Swann Seguin, Nicolas |
| author_facet | Chhatoi, Saroj Prasad Henrion, Didier Marx, Swann Seguin, Nicolas |
| contents | We prove that there is no relaxation gap between a quasi-dissipative nonlinear evolution equation in a Hilbert space and its linear Liouville equation reformulation on probability measures. In other words, strong and generalized solutions of such equations are unique in the class of measure-valued solutions. As a major consequence, non-convex numerical optimization over these non-linear partial differential equations can be carried out with the infinite-dimensional moment-SOS hierarchy with global convergence guarantees. This covers in particular all reaction-diffusion equations with polynomial nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy Chhatoi, Saroj Prasad Henrion, Didier Marx, Swann Seguin, Nicolas Analysis of PDEs Optimization and Control We prove that there is no relaxation gap between a quasi-dissipative nonlinear evolution equation in a Hilbert space and its linear Liouville equation reformulation on probability measures. In other words, strong and generalized solutions of such equations are unique in the class of measure-valued solutions. As a major consequence, non-convex numerical optimization over these non-linear partial differential equations can be carried out with the infinite-dimensional moment-SOS hierarchy with global convergence guarantees. This covers in particular all reaction-diffusion equations with polynomial nonlinearity. |
| title | Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2412.07361 |