An isoperimetric type problem for Bézier curves of degree n

We present an efficient algorithm, which solves an isoperimetric type problem in the class of Bézier curves of degree n>2. This algorithm requires to compute the maximal characteristic value and the corresponding principal vector of a regular pencil problem with block square matrices of dimension 2n−2. The coordinates of the principal vector determine the control points of the extremal curve, while the characteristic value gives the maximal area bounded by this curve.