  This article is devoted to one particular case of using universal accelerated
proximal envelopes to obtain computationally efficient accelerated versions of
methods used to solve various optimization problem setups. In this paper, we
propose a proximally accelerated coordinate descent method that achieves the
efficient algorithmic complexity of iteration and allows one to take advantage
of the problem sparseness. An example of applying the proposed approach to
optimizing a SoftMax-like function considered, for which the described method
allowing weaken the dependence of the computational complexity on the dimension
of the problem $n$ in $\mathcal{O}(\sqrt{n})$ times, and in practice
demonstrates a faster convergence in comparison with standard methods.
