标题： 一种加速的随机Bregman-Kaczmarz方法求解强凸线性约束优化问题 显示英文标题

标题： An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization

摘要： 本文提出了一种随机加速方法，用于求解具有线性约束的强凸函数最小化问题。 该方法属于Kaczmarz类方法，即每次迭代仅使用单个线性方程。 为了实现加速，我们利用了Kaczmarz方法与坐标下降法互为对偶这一事实。 我们将最近提出的随机坐标下降加速方法转移到原始空间。 该方法继承了许多加速坐标下降法的优秀特性，包括最坏情况下的收敛速率。 给出了所提出方法收敛性的理论分析。 数值实验表明，所提出的方法比现有方法更高效且更快地解决了相同的问题。 显示英文摘要

摘要： 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.