Lagrange multiplier

Lagrange multiplier is a mathematical optimization to obtain local maxima and minima subject to constraints, that is needed to understand regulatization L1 and L2.

maximize f(x,y) subject to g(x,y) = 0

f, g are continuous first partial derivatives

Then if $f(x_0,y_0)$ is a maxium of $f(x,y)$, then there exists $\lambda_0$ such that $\mathcal{L}(x_0, y_0, \lambda_0)$ is a stationary point (stationary points are those points where the partial derivatives of ${\mathcal {L}}$ are zero).

source: Lagrange multiplier