Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

In this paper, we study the problem of recovering a low-rank matrix from a number of random
linear measurements that are corrupted by outliers taking arbitrary values. We consider a …

As science and engineering have become increasingly data-driven, the role of optimization
has expanded to touch almost every stage of the data analysis pipeline, from signal and …

We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which
the objective function is weakly convex in the ambient Euclidean space. Such problems are …

Geometric model fitting is a fundamental task in computer vision, which serves as the pre-
requisite of many downstream applications. While the problem has a simple intrinsic …

We advance both the theory and practice of robust $\ell_p $-quasinorm regression for $ p\in
(0, 1] $ by using novel variants of iteratively reweighted least-squares (IRLS) to solve the …

We consider a class of Riemannian optimization problems where the objective is the sum of
a smooth function and a nonsmooth function, considered in the ambient space. This class of …

This paper is about the old Wahba problem in its more general form, which we call"
simultaneous rotation and correspondence search". In this generalization we need to find a …

This paper concerns dictionary learning, ie, sparse coding, a fundamental representation
learning problem. We show that a subgradient descent algorithm, with random initialization …

In this paper, we study the generalized subdifferentials and the Riemannian gradient
subconsistency that are the basis for non-Lipschitz optimization on embedded submanifolds …