Woosuk L. Jung

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

  • Woosuk L. Jung
  • Walaa M. Moursi
  • Henry Wolkowicz
    • Categories Combinatorial Optimization, Meta Heuristics, Semi-definite Programming

    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 for Generelized Jacobians with the ω-Condition Number

  • Woosuk L. Jung
  • David Torregrosa-Belén
  • Henry Wolkowicz
    • Categories Nonsmooth Optimization, Other Topics Tags , , ,

    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