
The Lagrangian, L, of a dynamical system is a mathematical function that summarizes the dynamics of the system. For a simple mechanical system, it is the value given by the kinetic energy of the particle minus the potential energy of the particle but it may be generalized to more complex systems. It is used primarily as a key component in the Eule...
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http://en.wikipedia.org/wiki/Lagrangian

For the mathematical program in standard form, the Lagrangian is the function: L(x, u, v) = f(x) - u g(x) - v h(x) for x in X and u >= 0. Note that the Lagrange Multiplier Rule can be written as the first-order conditions for (x*, u*,v*) to be a saddlepoint of L. In Lagrange's multiplier theorem (where X=R^n and g is vacuous), this is simply th...
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http://glossary.computing.society.informs.org/index.php?page=L.html

A function constructed in solving economic models that include maximization of a function (the 'objective function') subject to constraints. It equals the objective function minus, for each constraint, a variable 'Lagrange multiplier' times the amount by which the constraint is violated.
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http://www-personal.umich.edu/~alandear/glossary/l.html

a function describing the equations of motion for a system
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http://www.translationdirectory.com/glossaries/glossary303.php
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