Stochastic Methods for Composite and Weakly Convex Optimization Problems
研究了复合随机泛函（非光滑凸函数与光滑函数的组合）及弱凸随机泛函的最小化问题，提出了随机近线性算法和随机次梯度方法，证明其收敛到一阶稳定点，并在非光滑相位恢复问题上验证了有效性。
We consider minimization of stochastic functionals that are compositions of a (potentially) nonsmooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly convex functionals. We develop a family of stochastic methods---including a stochastic prox-linear algorithm and a stochastic (generalized) subgradient procedure---and prove that, under mild technical conditions, each converges to first order stationary points of the stochastic objective. We provide experiments further investigating our methods on nonsmooth phase retrieval problems; the experiments indicate the practical effectiveness of the procedures.