  The problem of convex optimization is studied. Usually in convex optimization
the minimization is over a d-dimensional domain. Very often the convergence
rate of an optimization algorithm depends on the dimension d. The algorithms
studied in this paper utilize dictionaries instead of a canonical basis used in
the coordinate descent algorithms. We show how this approach allows us to
reduce dimensionality of the problem. Also, we investigate which properties of
a dictionary are beneficial for the convergence rate of typical greedy-type
algorithms.
