Optimal low-rank matrix completion: Semidefinite relaxations and eigenvector disjunctions
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 …
recovers a given set of observations as accurately as possible. Unfortunately, existing …
Spectrally constrained optimization
We investigate how to solve smooth matrix optimization problems with general linear
inequality constraints on the eigenvalues of a symmetric matrix. We present solution …
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 …
we construct an analogous relax-then-sample strategy for low-rank optimization problems …
Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances
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 …
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 …
$\mathcal {S} $ under certain structural assumptions, where $\mathcal {S} $ which is defined …