论文标题
关于$ q $ - 随机坐标的汇总算法的非凸问题
On convergence of a $q$-random coordinate constrained algorithm for non-convex problems
论文作者
论文摘要
我们提出了一种随机坐标下降算法，用于优化由一个线性约束和变量上的简单界限的非凸目标函数。尽管在坐标下降算法的每次迭代中同时仅更新两个随机坐标是常见的，但是我们的算法允许更新任意数量的坐标数。我们提供了算法收敛的证明。当我们通过迭代更新更多坐标时，算法的收敛速率会提高。在不同优化问题的大规模实例上进行的数值实验表明，同时更新许多坐标的好处。
We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates simultaneously in each iteration of a coordinate descent algorithm, our algorithm allows updating arbitrary number of coordinates. We provide a proof of convergence of the algorithm. The convergence rate of the algorithm improves when we update more coordinates per iteration. Numerical experiments on large scale instances of different optimization problems show the benefit of updating many coordinates simultaneously.
