Woosuk L. Jung Preconditioning (scaling) is essential in many areas of mathematics, and in particular in optimization. In this work, we study the problem of finding an optimal diagonal preconditioner. We focus on minimizing two different notions of condition number: the classical, worst-case type, \(\kappa\)-condition number, and the more averaging motivated \(\omega\)-condition number. We provide affine based pseudoconvex … Read more
The simplified Wasserstein barycenter problem, also known as the cheapest hub problem, consists in selecting one point from each of \(k\) given sets, each set consisting of \(n\) points, with the aim of minimizing the sum of distances to the barycenter of the \(k\) chosen points. This problem is also known as the cheapest hub … Read more
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