4 accepted papers
We study the convergence rate of gradient-based local search methods for solving low-rank matrix recovery problems with general objectives in both symmetric and asymmetric cases, under the assumption of the restricted isometry property. First, we develop a new technique to verify the Polyak-Lojasiew…
In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search methods can find the ground truth with a small error. By ana…
This paper considers the global geometry of general low-rank minimization problems via the Burer-Monterio factorization approach. For the rank-$1$ case, we prove that there is no spurious second-order critical point for both symmetric and asymmetric problems if the rank-$2$ RIP constant $\delta$ is…
The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements. In this paper, we introduce a novel property named bound difference property (BDP) to study low-rank matrix recovery pr…