论文标题
通过半决赛编程的随机和循环坐标下降进行凸优化的随机和循环坐标下降的收敛速率分析
Convergence rate analysis of randomized and cyclic coordinate descent for convex optimization through semidefinite programming
论文作者
论文摘要
在本文中,我们研究了无限制优化问题的随机和循环坐标下降。在某些情况下,我们使用数值半决赛编程性能估计方法提高了已知的收敛速率。作为衍生产品,我们提供了一种分析线性系统高斯 - 赛义迭代方法最差的方法的方法,在该系统中,系数矩阵为阳性半芬酸盐,具有阳性对角线。
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation method. As a spin-off we provide a method to analyse the worst-case performance of the Gauss-Seidel iterative method for linear systems where the coefficient matrix is positive semidefinite with a positive diagonal.