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

Semidefinite programming (SDP) is a powerful framework from convex optimization that has
striking potential for data science applications. This paper develops a provably correct …

We consider semidefinite programs (SDPs) with equality constraints. The variable to be
optimized is a positive semidefinite matrix X of size n. Following the Burer‐Monteiro …

Smooth, non-convex optimization problems on Riemannian manifolds occur in machine
learning as a result of orthonormality, rank or positivity constraints. First-and second-order …

When solving large-scale semidefinite programs that admit a low-rank solution, an efficient
heuristic is the Burer--Monteiro factorization: instead of optimizing over the full matrix, one …

Riemannian Langevin algorithm for solving semidefinite programs Page 1 Bernoulli 29(4),
2023, 3093–3113 https://doi.org/10.3150/22-BEJ1576 Riemannian Langevin algorithm for …

Abstract The Burer-Monteiro method is one of the most widely used techniques for solving
large-scale semidefinite programs (SDP). The basic idea is to solve a nonconvex program in …

Orthogonal group synchronization is the problem of estimating elements from the orthogonal
group given some relative measurements. The least-squares formulation is nonconvex. To …

In this work, we consider the low-rank decomposition (SDPR) of general convex semidefinite
programming (SDP) problems that contain both a positive semidefinite matrix and a …

Semidefinite programming (SDP) with diagonal constraints arise in many optimization
problems, such as Max-Cut, community detection and group synchronization. Although …