We address randomized methods for convex optimization based on generating points uniformly distributed in a convex set. We estimate the rate of convergence for such methods and demonstrate the link with the center of gravity method. To implement such approach we exploit two modern Monte Carlo schemes for generating points which are approximately uniformly distributed in a given convex set. Both methods use boundary oracle to find an intersection of a ray and the set. The first method is Hit-and-Run, the second is sometimes called Shake-and-Bake. Numerical simulation results look very promising.