Minimization with orthogonality constraints (e.g., X'X = I) and/or spherical constraints (e.g., ||x||_2 = 1) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, ...

Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts ...

A set of vectors (or signals) are jointly sparse if their nonzero entries are commonly supported on a small subset of locations. Consider a network of agents which collaborative recover a set of joint sparse vectors. This ...

The Rayleigh-Ritz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively high-dimensional eigenspaces of large sparse matrices. Although operations involved in RR steps can be ...

The problem of finding p-harmonic flows arises in a wide range of applications including micromagnetics, liquid crystal theory, directional diffusion, and chromaticity denoising. In this paper, we propose an innovative ...

The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value ...

We derive and study a Gauss-Newton method for computing the symmetric low-rank product (SLRP) XXT, where X / Rnkfor k<n, that is the closest approximation to a given symmetric matrix A / Rnn in Frobenius norm. When A=BTB ...

In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations ...

The matrix separation problem aims to separate a low-rank matrix and a sparse matrix from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications. ...

The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; ...