Continuity properties of Chebyshev centers

Relative Chebyshev Centers in Hilbert Space

We characterize inner product spaces in terms of the relationship between the relative Chebyshev center of a set and the absolute Cheby-shev center of an associated set. A consequence of the characterization is that an existing nite algorithm can be adapted to calculate the center of a nite set relative to a nite dimensional aane space. We also discuss the case where the constraint set is nonli...

Continuity Properties of LQG

It is shown that the LQG optimal controller is a continuous function of the plant. The result is proved for a class of plants which contains the class of strictly proper nite-dimensional plants. The topology employed is the one generated by convergence of the closed loop transfer functions in an induced L 1 sense. This topology is slightly stronger than the usual (H 2) gap metric convergence on...

Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules

Klee sets and Chebyshev centers for the right Bregman distance

We systematically investigate the farthest distance function, farthest points, Klee sets, and Chebyshev centers, with respect to Bregman distances induced by Legendre functions. These objects are of considerable interest in Information Geometry and Machine Learning; when the Legendre function is specialized to the energy, one obtains classical notions from Approximation Theory and Convex Analys...

Mixing Properties of Mixed Chebyshev Polynomials

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