Approximation of the classical isoperimetric problem

Abstract

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.