On methods for obtaining solutions of fixed end-point problems in the calculus of variations

Abstract

Two methods for co nstructing solutions to t he problem of minimizing an integral in a certain class of arcs joining a pair of fixed points are proposed. One of t hese procedures is a generalization of Newton's method, while the other is a "gradient" method. Co ndition s for convergence to a strong r elat iv e mi nimum are given in both cases.