Lagrangian - Open Access .click

Physica Scripta, 2011
We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71–128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815–9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational ...
M.C. Nucci, P.G.L. Leach
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Lagrangian Subgradients

Management Science, 1970
There is a dual program linked with every nonlinear program. The dual objective function is called the Lagrangian; it is defined in terms of the original problem. This note presents a characterization of the Lagrangian subgradients under general conditions. The theorem follows from a result of Danskin [1] that can be used (see [2]) to characterize the
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Lagrangian-Perfect Hypergraphs

Annals of Combinatorics, 2023
For an \(r\)-graph \((r\ge2)\) \(G=(V,E)\) with \(V=[n]\), and \(\vec x=(x_1,\dots,x_n)\in[0,\infty)^n\), \(\lambda(G,\vec x)=\sum\limits_{e\in E}\prod\limits_{i\in e}x_i\); the Lagrangian is \(\lambda(G) =\max\{\lambda(G,\vec x):\vec x\in\Delta\}\), where \(\Delta=\{\vec x=(x_1,x_2,\dots,x_n)\in[0,1]^n:x_1+x_2+\dots+x_n=1\}\); the Lagrangian density \(
Yan, Zilong, Peng, Yuejian
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