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Continuity Of Metric Projection, Pólya Algorithm, Strict Best Approximation, And Tubularity Of Convex Sets, Robert Huotari, Wu Li

Mathematics & Statistics Faculty Publications

The notion of tubularity of a convex subset, K, of l∞ (n) was originally introduced to study the convergence of the Pólya algorithm. It is shown in the present paper that this geometric condition provides a characterization of thosed closed convex sets onto which the set-valued metric projection is continuous. In the development of this result, Rice′s strict best approximation is characterized in three new ways, and is shown, assuming tubularity of K, to be a continuous selection. The class of sets on which the Pólya algorithm is known to converge is enlarged to include …