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.

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。