quasi-newton matrices

A Dense initialization for limited-memory quasi-Newton methods

  • Johannes Brust
  • Oleg Burdakov
  • Jennifer B. Erway
  • Roummel F. Marcia
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    We consider a family of dense initializations for limited-memory quasi-Newton methods. The proposed initialization exploits an eigendecomposition-based separation of the full space into two complementary subspaces, assigning a different initialization parameter to each subspace. This family of dense initializations is proposed in the context of a limited-memory Broyden- Fletcher-Goldfarb-Shanno (L-BFGS) trust-region method that makes use … Read more

    On efficiently computing the eigenvalues of limited-memory quasi-Newton matrices

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

    In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any member of the Broyden convex class of updates. Our proposed method makes use of efficient updates to the QR factorization that … Read more