sherman-morrison-woodbury formula

On solving large-scale limited-memory quasi-Newton equations

  • Jennifer B. Erway
  • Roummel F. Marcia
    • Categories Nonlinear Optimization Tags , , , , , ,

    We consider the problem of solving linear systems of equations with limited- memory members of the restricted Broyden class and symmetric rank-one matrices. In this paper, we present various methods for solving these linear systems, and propose a new approach based on a practical implementation of the compact representation for the inverse of these limited-memory … Read more

    A modified nearly exact method for solving low-rank trust region subproblem

  • Zhaosong Lu
  • Renato D.C. Monteiro
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper we present a modified nearly exact (MNE) method for solving low-rank trust region (LRTR) subproblem. The LRTR subproblem is to minimize a quadratic function, whose Hessian is a positive diagonal matrix plus explicit low-rank update, subject to a Dikin-type ellipsoidal constraint, whose scaling matrix is positive definite and has the similar structure … Read more