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, and has numerous applications such as product recommendation. Unfortunately, existing methods for solving low-rank matrix completion are heuristics that, while highly scalable and often identifying high-quality solutions, do not possess any optimality guarantees. … Read more

A Stochastic Benders Decomposition Scheme for Large-Scale Data-Driven Network Design

Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a data-driven version where operational costs are uncertain and estimated on historical data. This problem is computationally challenging, and instances with as few as 50 nodes cannot be solved to optimality by current … Read more

Sparse PCA With Multiple Components

Sparse Principal Component Analysis is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. At its heart, this involves solving a sparsity and orthogonality constrained convex maximization problem, which is extremely computationally challenging. Most existing work address sparse PCA via heuristics … Read more

Decarbonizing OCP

Problem definition:  We present our collaboration with the OCP Group, one of the world’s largest producers of phosphate and phosphate-based products, in support of a green initiative designed to significantly reduce OCP’s carbon emissions. We study the problem of decarbonizing OCP’s electricity supply by installing a mixture of solar panels and batteries to minimize its … Read more