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 …

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 …

Despite the empirical success of using adversarial training to defend deep learning models
against adversarial perturbations, so far, it still remains rather unclear what the principles are …

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 …

This paper is concerned with finding a solution x to a quadratic system of equations yi=|< ai,
x>|^ 2, i= 1, 2,..., m. We prove that it is possible to solve unstructured quadratic systems in n …

We estimate n phases (angles) from noisy pairwise relative phase measurements. The task
is modeled as a nonconvex least-squares optimization problem. It was recently shown that …

This book revolves around the question of designing a matrix D∈ Rm× n called dictionary,
such that to obtain good sparse representations y≈ Dx for a class of signals y∈ Rm given …

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 …

A commonly used heuristic in non-convex optimization is Normalized Gradient Descent
(NGD)-a variant of gradient descent in which only the direction of the gradient is taken into …

In this note, we focus on smooth nonconvex optimization problems that obey:(1) all local
minimizers are also global; and (2) around any saddle point or local maximizer, the objective …