Discrepancy and convex programming

Abstract

The pertinence of convexity arguments in the study of discrepancy of sequences is exhibited. The usefulness of this viewpoint can be twofold. Firstly, it allows the interpretation of the problem of estimating the discrepancy as a problem in convex programming in important cases. Secondly, it helps to restrict the family of sets which have to be considered when evaluating the usual (or extreme) discrepancy and the isotrope discrepancy of sequences. In particular, in the latter case it suffices to look at a rather special class of convex polytopes. © 1972 Nicola Zanichelli Editore.