In the math optimization problem, the method of Lagrange multipliers is used as a tool for finding the local minima and maxima of a function subject to equality constraints. An example involves finding the maximum entropy distribution subject to given constraints.

This is best explained with an example. Let's say we have to maximize *K (x, y) = -x2 -y2 subject to y = x + 1*.

The constraint function is *g (x, y) = x-y+1=0*. The *L* multiplier then becomes this:

Differentiating with respect to *x*, *y*, and lambda, and setting to *0* we get the following:

Solving the preceding equations, we get *x=-0.5*, *y=0.5*, *lambda=-1*.