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Index theorems for graph-parametrized optimal control problems

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Andrei Agrachev, Stefano Baranzini, Ivan Beschastnyi

Optimization and Control · Submitted 24 Jan 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs.

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arXiv ID2201.09719 (version 1)
Pith IDLO3PHKT6, Pith's permanent record of this paper and its review
CitationAndrei Agrachev, Ivan Beschastnyi, Stefano Baranzini. "Index theorems for graph-parametrized optimal control problems." arXiv:2201.09719 (2022). https://pith.science/paper/LO3PHKT6
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.24 · compares with prior results 0.13 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

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.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. contribution 0.96 0.96 0.89 asserted 1.00
s1 Such theorems are useful in various physical and geometric applications. background 0.55 0.07 0.04 asserted 0.99
s2 Our formulas compute the difference of Morse indices of two Hessians related to two different graphs or two different sets of boundary conditions. contribution 0.54 0.93 0.41 asserted 1.00
s3 Several applications such as the iteration formulas or lower bounds for the index are proved. result 0.67 0.92 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original 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. Several applications such as the iteration formulas or lower bounds for the index are proved.

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