Nonsmooth rank-one symmetric matrix factorization landscape

TL;DR

This paper investigates the landscape of nonsmooth rank-one symmetric matrix factorization, revealing that it has no spurious second-order stationary points, which has implications for optimization and convergence.

Contribution

The paper characterizes the optimization landscape of nonsmooth rank-one symmetric matrix factorization, showing the absence of spurious second-order stationary points.

Findings

No spurious second-order stationary points in the landscape

Insights into optimization behavior for nonsmooth matrix factorization

Potential implications for algorithm design

Abstract

We consider nonsmooth rank-one symmetric matrix factorization. It has no spurious second-order stationary points.