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Stochastic Primal Dual Fixed Point Method for Composite Optimization
Journal of Scientific Computing ( IF 2.8 ) Pub Date : 2020-07-07 , DOI: 10.1007/s10915-020-01265-2
Ya-Nan Zhu , Xiaoqun Zhang

In this paper we propose a stochastic primal dual fixed point method for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method proposed in Chen et al. (Inverse Probl 29:025011, 2013) that does not require subproblem solving. Under some mild condition, the convergence is established based on two sets of assumptions: bounded and unbounded gradients and the convergence rate of the expected error of iterate is of the order \({\mathcal {O}}(k^{-\alpha })\) where k is iteration number and \(\alpha \in (0,1]\). Finally, numerical examples on graphic Lasso and logistic regressions are given to demonstrate the effectiveness of the proposed algorithm.



中文翻译:

随机原始对偶不动点复合优化

在本文中,我们提出了一种随机的原始对偶不动点方法,用于求解两个适当的下半连续凸函数之和,其中一个是复合函数。该方法基于Chen等人提出的原始对偶不动点方法。(Inverse Probl 29:025011,2013),不需要解决子问题。在某些温和条件下,基于两套假设建立有收敛性:有界和无界梯度,迭代期望误差的收敛率约为\({\ mathcal {O}}(k ^ {-\ alpha }} \)其中k是迭代数和\(\ alpha \ in(0,1] \)最后,给出了图形套索上的数值示例和逻辑回归,以证明该算法的有效性。

更新日期:2020-07-07
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