TWO DIRECT METHODS FOR OBTAINING SOLUTIONS TO VARIATIONAL PROBLEMS
Dean A. Carlson · International Game Theory Review · 2004
In this paper we compare two methods for obtaining solutions for free problems in the Calculus of Variations. The first appears at least as early as 1935 and is due to Carathéodory while the second, due to Leitmann, first appears in 1967. Both methods introduce the notion of equivalent variational problems. Using either approach, an auxiliary problem is obtained for which the solution is more easily obtained. We compare both approaches by using each to solve the same class of examples. We conclude our discussion by unifying the two approaches into one and illustrating this new method's potential through the use of an elementary example.