Lagrange multiplier

A Lagrangian multiplier is a constant, usually represented by the Greek symbol lambda (λ), which is part of the formula for finding an extreme value of a function f(x,y) subject to a constraint g(x,y). For example, the method of Lagrange multipliers can help determine the maximum area of a rectangle that can be fit inside a given circle represented by g(x,y) = x² + y².

The points at which extrema occur for a function f(x,y) subject to the constraint g(x,y) are the common solutions to:

$\nabla f=\left({\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}},{\frac {\partial f}{\partial z}}\right)=\lambda \nabla g$

and g(x,y) = 0.