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Continuous Selections for Metric Projections and Interpolating Subspaces


Wu Li

The existence of continuous selections for metric projections is the theoretical foundation of the existence of stable algorithms for computing best approximation elements. In this monograph we will give various intrinsic characterizations of subspaces of C o(T) which ensure the existence of continuous metric selections. Since the Chebyshev approximation is a special case of semi-infinite optimization, we hope that our study will give some insight to stability problems in semi-infinite optimization as well as parametric optimizations.
Contents: This monograph deals with various intrinsic characterizations of those subspaces G of C o(T) whose metric projections P G have continuous selections. We have a systematic development of the theory of the classical Chebyshev alternation phenomena and the strict best approximation introduced by J.R. Rice.