Lagrange multipliers without differentiability

Alex Rutar

The method of Lagrange multipliers is a well-known tool for computing local maxima of a function subject to constraints. One difficulty is that classical presentations rely on differentiability assumptions that can be difficulty or impossible to verify in practice. I will present the method of Lagrange multipliers with an emphasis on the underlying duality, but with no differentiability assumptions on the objective function or the constraints. Some hints as to why this is useful in practice may also be presented.