A dynamic inversion of the classical variational problems (Q797133)

In a recent paper [ibid. 82, 49-65 (1981; Zbl 0467.49021)] the author associated to a (minimum) optimal control problem an equivalent (maximum) optimal control problem and called the latter the inverse problem. The point of view is that of dynamic programming. In the present paper he applies the above ideas to the simplest problem in the classical calculus of variations and gives as explicit examples the inverse problems of the shortest path problem, the minimum surface of revolution problem and certain quadratic problems.