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

Accelerated Proximal Envelopes: Application to the Coordinate Descent Method