Index theorems for graph-parametrized optimal control problems
| Autor: | Andrei Agrachev, Stefano Baranzini, Ivan Beschastnyi |
|---|---|
| Přispěvatelé: | Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Universidade de Aveiro, The work of the third author was supported through the CIDMA Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology ('FCT - Fundacao para a Ciencia e a Tecnologia') within the project UIDP/04106/2020. |
| Rok vydání: | 2023 |
| Předmět: |
Mathematics - Differential Geometry
Differential Geometry (math.DG) Optimization and Control (math.OC) Applied Mathematics FOS: Mathematics General Physics and Astronomy Statistical and Nonlinear Physics [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Mathematics - Optimization and Control Mathematical Physics |
| Zdroj: | Nonlinearity. 36:2792-2838 |
| ISSN: | 1361-6544 0951-7715 |
| Popis: | In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two Hessians related to two different graphs or two different sets of boundary conditions. Several applications such as the iteration formulas or lower bounds for the index are proved. 30 pages, 4 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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