%0 Journal Article
%T When Are Nonconvex Problems Not Scary?
%A Ju Sun
%A Qing Qu
%A John Wright
%J Mathematics
%D 2015
%I arXiv
%X In this paper, we focus on nonconvex optimization problems with no "spurious" local minimizers, and with saddle points of at most second-order. Concrete applications such as dictionary learning, phase retrieval, and tensor decomposition are known to induce such structures. We describe a second-order trust-region algorithm that provably converges to a local minimizer in polynomial time. Finally we highlight alternatives, and open problems in this direction.
%U http://arxiv.org/abs/1510.06096v1