Abstract
A characterization of those linear semi-infinite optimization problems which have a unique resp. strongly unique solution for all restriction functions is given. This result is applied to best approximation of continuous functions. The classical theorem of Haar in Chebyshev approximation follows as a special case. More over it is shown that global unicity in one-sided L1-approximation is equivalent to the non-existence of certain quadrature formulas. Using this characterization a general non-unicity result on one-sided L1-approximation is obtained.
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