论文标题
非平滑和非凸优化的乘数的随机交替方向方法
A Stochastic Alternating Direction Method of Multipliers for Non-smooth and Non-convex Optimization
论文作者
论文摘要
乘数的交替方向方法（ADMM）是一种流行的一阶方法，由于其简单性和效率。但是，类似于其他近端分裂方法，当要解决的优化问题的规模变得较大时，ADMM的性能会大大降低。在本文中，我们考虑将ADMM与一类随机梯度相结合，并降低了差异，以解决大规模的非凸和非平滑优化问题。生成序列的全局收敛是在对象函数满足Kurdyka-lojasiewicz（KL）属性的额外假设下建立的。对图引导的融合拉索和计算机断层扫描进行了数值实验，以证明所提出的方法的性能。
Alternating direction method of multipliers (ADMM) is a popular first-order method owing to its simplicity and efficiency. However, similar to other proximal splitting methods, the performance of ADMM degrades significantly when the scale of the optimization problems to solve becomes large. In this paper, we consider combining ADMM with a class of stochastic gradient with variance reduction for solving large-scale non-convex and non-smooth optimization problems. Global convergence of the generated sequence is established under the extra additional assumption that the object function satisfies Kurdyka-Lojasiewicz (KL) property. Numerical experiments on graph-guided fused Lasso and computed tomography are presented to demonstrate the performance of the proposed methods.
