Optimal low-rank matrix completion: Semidefinite relaxations and eigenvector disjunctions

D Bertsimas, R Cory-Wright, S Lo… - arXiv preprint arXiv …, 2023 - arxiv.org
Low-rank matrix completion consists of computing a matrix of minimal complexity that
recovers a given set of observations as accurately as possible. Unfortunately, existing …

Spectrally constrained optimization

C Garner, G Lerman, S Zhang - Journal of Scientific Computing, 2024 - Springer
We investigate how to solve smooth matrix optimization problems with general linear
inequality constraints on the eigenvalues of a symmetric matrix. We present solution …

Improved Approximation Algorithms for Low-Rank Problems Using Semidefinite Optimization

R Cory-Wright, J Pauphilet - arXiv preprint arXiv:2501.02942, 2025 - arxiv.org
Inspired by the impact of the Goemans-Williamson algorithm on combinatorial optimization,
we construct an analogous relax-then-sample strategy for low-rank optimization problems …

Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances

J Wang, M Boedihardjo, Y Xie - arXiv preprint arXiv:2405.15441, 2024 - arxiv.org
Optimal transport has been very successful for various machine learning tasks; however, it is
known to suffer from the curse of dimensionality. Hence, dimensionality reduction is …

A Geometric Perspective on the Closed Convex Hull of Some Spectral Sets

R Zhao - arXiv preprint arXiv:2405.14143, 2024 - arxiv.org
We propose a geometric approach to characterize the closed convex hull of a spectral set
$\mathcal {S} $ under certain structural assumptions, where $\mathcal {S} $ which is defined …