Perturbation of Sets and Centers

Authors:
E. Alvoni;P. L. Papini
Affiliations:
Dipartimento di Matematica, Applicata alle Scienze Economiche e Sociali, Bologna I-40126;Dipartimento di Matematica, Piazza Porta, Bologna I-40126
Venue:
Journal of Global Optimization
Year:
2005

Citing 4
Cited 2

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Abstract

Given a bounded set A, a Chebyshev center (when it exists) is---in some sense---a candidate to give a global information on the set. Finding the centers of A is of great importance for applications. In many cases, it is very important to understand how they change when the set A is perturbed. Our main result is a new characterization of Hilbert spaces: in fact, we will show that the best estimate we can give in these spaces, concerning perturbations of sets, cannot be expected outside this class of spaces. Moreover, we collect, we partly sharpen and we reprove in a simple way most known results.