Gradient-free prox-methods with inexact oracle for stochastic convex   optimization problems on a simplex
  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. 
Alexander Gasnikov and Anastasia Lagunovskaya and Ilnura Usmanova and   Fedor Fedorenko
math.OC