Digital filter design
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
A semidefinite framework for trust region subproblems with applications to large scale minimization
Mathematical Programming: Series A and B
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Trust-region methods
The mathematics of computerized tomography
The mathematics of computerized tomography
A Trust-Region Approach to the Regularization of Large-Scale Discrete Forms of Ill-Posed Problems
SIAM Journal on Scientific Computing
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
SIAM Journal on Optimization
Minimization of a Large-Scale Quadratic Function Subject to a Spherical Constraint
SIAM Journal on Optimization
On Some Properties of Quadratic Programs with a Convex Quadratic Constraint
SIAM Journal on Optimization
Solving the Trust-Region Subproblem using the Lanczos Method
SIAM Journal on Optimization
Minimizing a Quadratic Over a Sphere
SIAM Journal on Optimization
A large-scale trust-region approach to the regularization of discrete ill-posed problems
A large-scale trust-region approach to the regularization of discrete ill-posed problems
Regularization using a parameterized trust region subproblem
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Solving the quadratic trust-region subproblem in a low-memory BFGS framework
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
CARD: a decision-guidance framework and application for recommending composite alternatives
Proceedings of the 2008 ACM conference on Recommender systems
Block relaxation and majorization methods for the nearest correlation matrix with factor structure
Computational Optimization and Applications
Accelerating the LSTRS Algorithm
SIAM Journal on Scientific Computing
Computational Optimization and Applications
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A MATLAB 6.0 implementation of the LSTRS method is presented. LSTRS was described in Rojas et al. [2000]. LSTRS is designed for large-scale quadratic problems with one norm constraint. The method is based on a reformulation of the trust-region subproblem as a parameterized eigenvalue problem, and consists of an iterative procedure that finds the optimal value for the parameter. The adjustment of the parameter requires the solution of a large-scale eigenvalue problem at each step. LSTRS relies on matrix-vector products only and has low and fixed storage requirements, features that make it suitable for large-scale computations. In the MATLAB implementation, the Hessian matrix of the quadratic objective function can be specified either explicitly, or in the form of a matrix-vector multiplication routine. Therefore, the implementation preserves the matrix-free nature of the method. A description of the LSTRS method and of the MATLAB software, version 1.2, is presented. Comparisons with other techniques and applications of the method are also included. A guide for using the software and examples are provided.