The Adaption Problem for Nonsymmetric Convex Sets

Abstract

We study the problem of optimal recovery in the case of a nonsymmetric convex class of functions. We compare adaptive and nonadaptive methods and prove a bound on how much better adaptive methods can be. We use new inequalities between Gelfand widths and Bernstein widths and new relations between these widths and optimal error bounds for adaptive and nonadaptive methods, respectively.