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 optimization problems over the Stiefel manifold whose objective function is the
summation of a smooth function and a nonsmooth function. Existing methods for solving this …

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 …

The problem of estimating the phases (angles) of a complex unit-modulus vector z from their
noisy pairwise relative measurements C=zz^*+σW, where W is a complex-valued Gaussian …

We consider optimization problems over the Stiefel manifold whose objective function is the
summation of a smooth function and a nonsmooth function. Existing methods for solving this …

Various applications involve assigning discrete label values to a collection of objects based
on some pairwise noisy data. Due to the discrete—and hence nonconvex—structure of the …

Group synchronization asks to recover group elements from their pairwise measurements. It
has found numerous applications across various scientific disciplines. In this work, we focus …

The problem of optimizing a quadratic form over an orthogonality constraint (QP-OC for
short) is one of the most fundamental matrix optimization problems and arises in many …

This paper considers general rank-constrained optimization problems that minimize a
general objective function over the set of rectangular matrices that have rank at most r. To …

The problem of synchronization over a group G aims to estimate a collection of group
elements G 1⁎,…, G n⁎∈ G based on noisy observations of a subset of all pairwise ratios of …