# Variational calculus

### From Glossary

An approach to solving a class of optimization problems that seek a *functional* to make some integral function an extreme. Given
is smooth, then the classical unconstrained problem is to find to minimize (or maximize) the following function:

An example is a min arc length, where Using the Euler-Lagrange equation, the solution is where and are determined by *boundary conditions*:

If constraints take the form this is called the
*problem of Lagrange*; other forms are possible.