Constrained optimal location

A Chebyshev center of a set A in a normed space is;a location that minimizes the maximum distance to the set A. In many applications, this center may be regarded as an optimal location. In an inner product space, we characterize the linearly constrained optimal location in terms of the unconstrained optimal location of an associated set land show that this characterization is always possible if and only if the norm is induced by an inner product). We then use this characterization to design a finite algorithm for the calculation of the constrained optimal location of a finite point set. We conclude by demonstrating that the guarantee of convergence of this algorithm characterizes inner-product space.