Nontrivial extreme networks. Singularities of Lagrange functions and criterion of extremality

Alexandr O. Ivanov, Hông Vân Lê, and Alexey A. Tuzhilin

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Submission date: 06. Jul. 1999
Pages: 20
published as: Nontrivial critical networks : singularities of Lagrangians and a criterion for criticality.
In: Mathematical notes, 69 (2001) 3-4, p. 514 - 526 
DOI number (of the published article): 10.1023/A:1010260230867
published as: Nontrivial critical networks. Singularities of Lagrangians and a criterion for criticality.
In: Matematiceskie zametki, 69 (2001) 4, p. 566-580 
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Abstract:
In this note we consider the following problem

• what Lagrangians' properties lead to the existence of nontrivial branching extremals,
• what is the local structure of the branching extremals.

It turns out that the existence of nontrivial extreme networks is related closely with the presence of singularities of Lagrangian. For an wide class of Lagrangian we obtain a criterion of networks' extremality.