Exact Solutions for the NP-hard Wasserstein Barycenter Problem using a Doubly Nonnegative Relaxation and a Splitting Method

\(\) The simplified Wasserstein barycenter problem consists in selecting one point from \(k\) given sets, each set consisting of \(n\) points, with the aim of minimizing the sum of distances to the barycenter of the \(k\) points chosen. This problem is known to be NP-hard. We compute the Wasserstein barycenter by exploiting the Euclidean distance … Read more

Preconditioning for Generelized Jacobians with the ω-Condition Number

Preconditioning is essential in iterative methods for solving linear systems of equations. We study a nonclassic matrix condition number, the ω-condition number, in the context of optimal conditioning for low rank updating of positive definite matrices. For a positive definite matrix, this condition measure is the ratio of the arithmetic and geometric means of the … Read more