10. Extension of the Lagrange problem

10.1 Functional dependent on a single function

So far, we've considered functions that qualify as extremal to be continuous, as well as their first derivatives. We're going to extend the class of admissible functions to include those that are continuous and have piecewise continuous first derivatives, i.e. first derivatives that are continuous except at a finite number of points. The extremal then has an angular point. This is known as a broken extremal.

10.1.1 Better optimization

Consider...