In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [8, 11] for minimizing the sum of a smooth convex function and a blockseparable convex function. In particular, we extend Nesterov's technique developed in [8] for analyzing the RBCD method for minimizing a smooth convex function over a block-separable closed convex set to the aforementioned more general problem and obtain a sharper expected-value type of convergence rate than the one implied in [11] . Also, we obtain a better high-probability type of iteration complexity, which improves upon the one in [11] by at least the amount O(n/ǫ), where ǫ is the target solution accuracy and n is the number of problem blocks. In addition, for unconstrained smooth convex minimization, we develop a new technique called randomized estimate sequence to analyze the accelerated RBCD method proposed by Nesterov [8] and establish a sharper expected-value type of convergence rate than the one given in [8] .
REF present a sharper convergence analysis of Nesterov's method using a randomized estimate sequence framework.
On the Complexity Analysis of Randomized Block-Coordinate Descent Methods
ArXiv
ArXiv
Mathematics Computer Science