随机Bregman ADMM及其在训练具有离散结构的支持向量机中的应用

A stochastic Bregman ADMM with its application in training sparse structure SVMs

针对具有多块可分结构的非凸优化问题提出了一类新的随机Bregman交替方向乘子法,在周期更新规则下,证明了该算法的渐进收敛性;在随机更新的规则下,几乎确定的渐进收敛性得以证明。数值实验结果表明,该算法可有效训练具有离散结构的支持向量机。

A new stochastic Bregman multiplier alternating direction method(SB-ADMM)is proposed for non-convex optimization problems with multiple separable blocks.It is shown that the sequence produced by the S-B-ADMM under the periodic update rule converges asymptotically to a stationary solution of the Lagrangian function of the original problem.Under the random update rule,we prove the almost surely convergence of the sequence produced by the S-B-ADMM.Numerical experiments results illustrate the feasibility of the S-B-ADMM for training sparse structural support vector machines.