Keiichi Morikuni

Error estimate for regularized optimal transport problems via Bregman divergence

  • Keiichi Morikuni
  • Koya Sakakibara
  • AsukaTAKATSU
    • Categories Convex and Nonsmooth Optimization, Linear Programming Tags , , ,

    Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the required properties for Bregman divergences, provide a non-asymptotic error estimate for the regularized problem, and show that the error estimate becomes … Read more

    Implementation of Interior-point Methods for LP based on Krylov Subspace Iterative Solvers with Inner-iteration Preconditioning

  • Yiran Cui
  • Takashi Tsuchiya
  • Ken Hayami
  • Keiichi Morikuni
    • Categories Linear Programming, Linear, Cone and Semidefinite Programming Tags , , ,

    We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe ill-conditioning of linear equations solved in the final phase of interior-point iterations. The employed Krylov subspace methods do not suffer from rank-deficiency and therefore no … Read more