Lagrange Multipliers

• strategy to find local maxima and minima of a function
• subject to a set of constraints

Definition

Want the maximum or minimum of function $f(x)$ subject to the equality constraint $g(x)=0$

Now partial derivatives set to $0$:

The solution is always a saddle point of the initial Lagrangian function $\mathcal{L}(x,\lambda )$