Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization
研究了一种随机块坐标下降算法在凸复合优化中的收敛性，证明了迭代几乎必然收敛到最优解，并给出了函数值的次线性收敛率和在误差界条件下的线性收敛率。
Abstract 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. Under the same condition strong convergence of the iterates is provided as well as their linear convergence rate.