Approximation of the classical isoperimetric problem

Hestenes' method of multipliers is used to approximate the classical isoperimetric problem. A suitable sufficiency theorem is first applied to obtain minimizing arcs for a family of unconstrained problems. Given an initial estimate of the Lagrange multipliers, a convergent sequence of arcs is generated. They are minimizing with respect to members of the above family, and their limit is the solution to the original isoperimetric problem.The preparation of this paper was sponsored in part by the U.S. Army Research Office under Grant DA-31-124-ARO(D)-355.