Category:Examples of Use of Lagrange's Method of Multipliers

This category contains examples of Lagrange's Method of Multipliers.

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 $\lambda_i$.