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. Some applications such as the iteration formulas and lower bounds for the index are proved.

Index theorems for graph-parametrized optimal control problems

Baranzini S.
;
2023-01-01

Abstract

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. Some applications such as the iteration formulas and lower bounds for the index are proved.
2023
36
5
2792
2838
constrained optimization; metric graph; Morse index; second variation
Agrachev A.; Baranzini S.; Beschastnyi I.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/2011450
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