Category:Definitions/Lagrange's Method of Multipliers

This category contains definitions related to Lagrange's Method of Multipliers.
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Lagrange's method of multipliers is a technique for finding maxima or minima of a real-valued function $\map f {x_1, x_2, \ldots, x_n}$ subject to one or more equality constraints $\map {g_i} {x_1, x_2, \ldots, x_n} = 0$.

The solution is found by minimizing:

$L = f + \lambda_1 g_1 + \lambda_2 g_2 + \cdots$

with respect to the $x_i$ and $\lambda_i$.