Lagrange Multipliers
Overview
The method of Lagrange multipliers is used to solve optimization problems when there is a multi-variable function to
be maximized/minimized and there are a number of constraints.
Statement of the Theorem
Given a function {% f(x_1,...,x_n) %} with m constraints
{% g_1(x_1,...,x_n)=0, ..., g_m(x_1,...,x_n)=0 %} with m<n, then
there exist {% \lambda_1, ..., \lambda_m %} such that
{% \nabla f = \lambda_1 \nabla g_1 , ..., \lambda_m \nabla g_m %}
