Parallel block coordinate descent methods with identification strategies
提出一种并行块坐标下降方法，通过识别非零坐标来聚焦计算，适用于大规模正则化回归问题，并给出收敛性证明和数值实验。
Abstract This work presents a parallel variant of the algorithm introduced in [ Acceleration of block coordinate descent methods with identification strategies , Comput. Optim. Appl. 72(3):609–640, 2019] to minimize the sum of a partially separable smooth convex function and a possibly nonsmooth block-separable convex function under simple constraints. The proposed method achieves higher efficiency by using a strategy to identify nonzero coordinates, thereby allowing the computational effort to be focused via a nonuniform probability distribution in block selection. Parallelization is achieved by extending theoretical results from Richtárik and Takáč [ Parallel coordinate descent methods for big data optimization , Math. Prog. Ser. A 156:433–484, 2016]. We present convergence results and comparative numerical experiments on regularized regression problems using both synthetic and real datasets.