In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain acceleration we build on the fact that the Kaczmarz method is dual to a coordinate descent method. We use a recently proposed acceleration method for the randomized coordinate descent and transfer it to the primal space. This method inherits many of the attractive features of the accelerated coordinate descent method, including its worst-case convergence rates. A theoretical analysis of the convergence of the proposed method is given. Numerical experiments show that the proposed method is more efficient and faster than the existing methods for solving the same problem.

翻译：本文针对线性约束下强凸函数的最小化问题，提出了一种随机加速方法。该方法属于Kaczmarz类型，即在每次迭代中仅使用单个线性方程。为实现加速，我们基于Kaczmarz方法与坐标下降法对偶这一事实，将最近提出的随机坐标下降加速方法转换到原始空间。该方法继承了加速坐标下降法的诸多优良特性，包括其最坏情况收敛速率。本文给出了所提方法收敛性的理论分析。数值实验表明，在求解相同问题时，所提方法比现有方法更高效、更快速。