Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy
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.
Authors
- Saroj Prasad Chhatoi (ORCID: https://orcid.org/0000-0002-1187-3689)
- Swann Marx (ORCID: https://orcid.org/0000-0002-0722-3560)
- Nicolas Seguin (ORCID: https://orcid.org/0000-0001-7783-9849)
- Didier Henrion (ORCID: https://orcid.org/0000-0001-6735-7715)
Institutions
- École Centrale de Nantes (FR)
- Centre National de la Recherche Scientifique (FR)
- Université Fédérale de Toulouse Midi-Pyrénées (FR)
- Laboratoire d'Analyse et d'Architecture des Systèmes (FR)
- Université de Montpellier (FR)
- Laboratoire des Sciences du Numérique de Nantes (FR)
- Nantes Université (FR)
Publication Details
- Journal
- Discrete and Continuous Dynamical Systems
- Published
- 2025-01-01
- DOI
- https://doi.org/10.3934/dcds.2025051
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- Agence Nationale de la Recherche