  In the paper we show that euclidian randomization in some situations (i.e.
for gradient-free method on a simplex) can be as good as the randomization on
the unit sphere in 1-norm. That is on the simplex example we show that for
gradient-free methods the choise of the prox-structure and the choise of a way
of randomization have to be connected to each other. We demonstrate how it can
be done in an optimal way. It is important that we consider inexact oracle.
