We study the problem of optimal recovery in the case of a nonsymmetric
convex class of functions. We compare adaptive and nonadaptive method
s 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 a
nd nonadaptive methods, respectively. (C) 1995 Academic Press, Inc.