ec 2 01 2 MSS : MATLAB SOFTWARE FOR L - BFGS TRUST - REGION SUBPROBLEMS FOR LARGE - SCALE OPTIMIZATION JENNIFER
نویسنده
چکیده
A MATLAB implementation of the Moré-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 Moré-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use of a recently proposed stable fast direct method for solving large shifted BFGS systems of equations [9, 8]. This MATLAB implementation is a matrix-free iterative method for large-scale optimization. Numerical experiments show that the MSS method is able to compute solutions to high accuracy.
منابع مشابه
A limited memory adaptive trust-region approach for large-scale unconstrained optimization
This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newt...
متن کاملLstrs: Matlab Software for Large-scale Trust-region Subproblems and Regularization
We describe a MATLAB implementation [6] of the method LSTRS [5] for the large-scale trust-region subproblem:
متن کاملSolving the quadratic trust-region subproblem in a low-memory BFGS framework
We present a new matrix-free method for the large-scale trust-region subproblem, assuming that the approximate Hessian is updated by the L-BFGS formula with m = 1 or 2. We determine via simple formulas the eigenvalues of these matrices and, at each iteration, we construct a positive definite matrix whose inverse can be expressed analytically, without using factorization. Consequently, a directi...
متن کاملOn solving L-SR1 trust-region subproblems
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 ShermanMorrison-Woodbury formula to ...
متن کاملA Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations
In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that ...
متن کامل