论文标题
用于凸复合优化的异步块坐标前向下算法的收敛
Convergence of an Asynchronous Block-Coordinate Forward-Backward Algorithm for Convex Composite Optimization
论文作者
论文摘要
在本文中，我们研究了一个随机的块坐标下降算法的收敛性，以最大程度地减少复合凸观物镜的最小化，其中块状坐标是根据任意概率分布异步和随机更新的。我们证明，该算法产生的迭代形成了随机的准式序列，因此几乎可以肯定地收敛到目标函数的最小化器。此外，我们证明了在TSENG类型的误差结合条件下，对函数值的期望值和期望的线性收敛速率的一般均值收敛速率。
In this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex objective function, where the block-coordinates are updated asynchronously and randomly according to an arbitrary probability distribution. We prove that the iterates generated by the algorithm form a stochastic quasi-Fejér sequence and thus converge almost surely to a minimizer of the objective function. Moreover, we prove a general sublinear rate of convergence in expectation for the function values and a linear rate of convergence in expectation under an error bound condition of Tseng type.
