作者
Shixiang Chen, Zengde Deng, Shiqian Ma, Anthony Man-Cho So
发表日期
2021/7/26
期刊
IEEE Transactions on Signal Processing
出版商
IEEE
简介
We consider the problem of minimizing the l 1 norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well explored. In this paper, we show how the manifold structure of the sphere can be exploited to design fast algorithms with provable guarantees for tackling this problem. Specifically, our contribution is fourfold. First, we present a manifold proximal point algorithm (ManPPA) for the problem and show that it converges at a global sublinear rate. Furthermore, we show that ManPPA can achieve a local quadratic convergence rate when applied to sharp instances of the problem. Second, we develop a semismooth Newton-based inexact augmented …
学术搜索中的文章
S Chen, Z Deng, S Ma, AMC So - IEEE Transactions on Signal Processing, 2021