Optimization over Matrices: From Data Science to Quantum Computing

Overview

Matrix Optimization problems are optimization instances over matrix variables. A prime example is semidefinite programming (SDP) in which one minimizes linear functionals over constraint sets specified via the intersection of the cone of positive definite matrices with an affine space. Matrix optimization problems, and specifically SDPs, have found applications in a wide range of areas.

Two prominent examples are in quantum computing and in the data sciences: In quantum computing, a basic object of interest is a density matrix — these describe quantum systems and are specified as matrices which are positive semidefinite with trace one. In the data sciences, SDPs offer a powerful and principled way to derive convex relaxations for constraints that are otherwise intractable to express. Prominent examples include low-rank constraints, dealing with rotations and rigid motions, as well as problems where group invariance or equivariance arise.

The goal of this workshop is to bring together researchers from these seemingly different communities who speak the common language of matrix optimization. The goal is to learn about the key advances and challenges in each other’s domain — whether in terms of modelling, computational, or analytical — in the hope that these exchanges may initiate new directions we have overlooked.