limited memory quasi-newton methods

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

    ALGORITHM XXX: SC-SR1: MATLAB SOFTWARE FOR SOLVING SHAPE-CHANGING L-SR1 TRUST-REGION SUBPROBLEMS

  • Johannes Brust
  • Oleg Burdakov
  • Jennifer B. Erway
  • Roummel F. Marcia
  • Ya-xiang Yuan
    • Categories Unconstrained Optimization Tags , , , , ,

    We present a MATLAB implementation of the shape-changing sym- metric rank-one (SC-SR1) method that solves trust-region subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix. The method takes advantage of two shape-changing norms [4, 3] to decompose the trust-region subproblem into two separate problems. Using one of … Read more

    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

    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

    On Solving L-SR1 Trust-Region Subproblems

  • Johannes Brust
  • Jennifer B. Erway
  • Roummel F. Marcia
    • Categories Optimization Software and Modeling Systems, Unconstrained Optimization Tags , , ,

    In this article, we consider solvers for large-scale trust-region subproblems when the quadratic model is defined by a limited-memory symmetric rank-one (L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact representation of L-SR1 matrices. Our approach makes use of both an orthonormal basis for the eigenspace of the L-SR1 matrix and the Sherman- … Read more

    MSS: MATLAB software for L-BFGS trust-region subproblems for large-scale optimization

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

    A MATLAB implementation of the More’-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the More’-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use … Read more

    A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs

  • Samuel Burer
  • Renato D.C. Monteiro
  • Yin Zhang
    • Categories Combinatorial Optimization, Semi-definite Programming, Unconstrained Optimization Tags , , , ,

    The authors of this paper recently introduced a transformation \cite{BuMoZh99-1} that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods to handle efficiently. Based … Read more