lagrange multiplier with interval constraint Given a function $g(x,y,z)$ we need to maximize it given constraints $a<x<b, a<y<b$. 
If the constraints were given as a function $f(x,y,z)$ the following equation could be used. 
$\nabla f(x,y,z)  = \lambda \nabla g(x,y,z)$
How would I set up the initial equation given an interval constraint. Or how would I turn the interval constraint into a function constraint.
EDIT:: Added $a<y<b$ to the constraints.

Maximize $g$ ignoring the constraint. If the solution fulfills the constraint, you're done. If not, there's no maximum, since it would have to lie on the boundary, but the boundary is excluded by the constraint.
