Substantial progress has been made recently on develo** provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

We consider the problem of recovering a complete (ie, square and invertible) matrix A 0,
from Y∈ R n× p with Y= A 0 X 0, provided X 0 is sufficiently sparse. This recovery problem is …

Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

Matrix completion is a basic machine learning problem that has wide applications,
especially in collaborative filtering and recommender systems. Simple non-convex …

Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …

We consider a family of algorithms that successively sample and minimize simple stochastic
models of the objective function. We show that under reasonable conditions on …

We show that there are no spurious local minima in the non-convex factorized
parametrization of low-rank matrix recovery from incoherent linear measurements. With …

We consider the problem of learning a one-hidden-layer neural network: we assume the
input $ x\in\mathbb {R}^ d $ is from Gaussian distribution and the label $ y= a^\top\sigma …

Nesterov's accelerated gradient descent (AGD), an instance of the general family of
“momentum methods,” provably achieves faster convergence rate than gradient descent …

We consider the minimization of a cost function f on a manifold using Riemannian gradient
descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality …