Fractional Brownian Motion

Appendix 2 Evaluation of the Chebyshev Center of a Set of Points in the Euclidean Space

The Chebyshev center of a set is defined in section 1.8.2 in Chapter 1 (see Definition 1.2). To find the Chebyshev center of a finite set is to minimize over . Note that the criterion function and its square are convex.

Before we present the algorithm for finding the Chebyshev center, we state auxiliary optimization problems and present subroutines for finding their solutions. They are: the problem of the hypersphere of minimal radius that contains a given finite set and two constrained least squares problems. Then, we find necessary and sufficient conditions for the point to be the Chebyshev center of a finite set and formulate the dual problem. This immediately reduces the Chebyshev center problem to the fully constrained least squares (FCLS) problem. Then, we present two algorithms for finding the Chebyshev center of a finite set of affinely independent points. Each of the Chebyshev center algorithms ...