STOCHASTIC METHODS FOR COMPOSITE AND WEAKLY CONVEX OPTIMIZATION PROBLEMS
STOCHASTIC METHODS FOR COMPOSITE AND WEAKLY CONVEX OPTIMIZATION PROBLEMS
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DOI：
10.1137/17m1135086
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发表时间：
2018-01-01
影响因子：
3.1
通讯作者：
Ruan, Feng
中科院分区：
文献类型：
--
作者：
Duchi, John C.;Ruan, Feng
我们考虑最小化的随机泛函的组成（潜在的）非光滑凸函数h和光滑函数c，更一般地说，随机弱凸泛函。我们开发了一个家庭的随机方法，包括一个随机的非线性算法和随机（广义）次梯度过程，并证明，在温和的技术条件下，每个收敛到一阶平稳点的随机目标。我们提供的实验进一步调查我们的方法对非光滑相位恢复问题，实验表明的程序的实际有效性。
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.