LSTRS
Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization 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.
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 14 articles )
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Sorted by year (- Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang: A Krylov subspace method for large-scale second-order cone linear complementarity problem (2015)
- Pong, Ting Kei; Wolkowicz, Henry: The generalized trust region subproblem (2014)
- Gratton, Serge; Gürol, Selime; Toint, Philippe L.: Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems (2013)
- Landi, G.; Piccolomini, E.Loli: A feasible direction method for image restoration (2012)
- Lampe, J.; Rojas, M.; Sorensen, D.C.; Voss, H.: Accelerating the LSTRS algorithm (2011)
- Li, Qingna; Qi, Houduo; Xiu, Naihua: Block relaxation and majorization methods for the nearest correlation matrix with factor structure (2011)
- Piccolomini, E.Loli; Zama, F.: An iterative algorithm for large size least-squares constrained regularization problems (2011)
- Lampe, Jörg; Voss, Heinrich: Solving regularized total least squares problems based on eigenproblems (2010)
- Erway, Jennifer B.; Gill, Philip E.; Griffin, Joshua D.: Iterative methods for finding a trust-region step (2009)
- Apostolopoulou, M.S.; Sotiropoulos, D.G.; Pintelas, P.: Solving the quadratic trust-region subproblem in a low-memory BFGS framework (2008)
- Rojas, Marielba; Santos, Sandra A.; Sorensen, Danny C.: Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization. (2008)
- Brezhneva, O.A.; Tret’yakov, A.A.: P-factor-approach to degenerate optimization problems (2006)
- Kearsley, Anthony J.: Matrix-free algorithm for the large-scale constrained trust-region subproblem (2006)
- Eldén, L.; Hansen, P.C.; Rojas, M.: Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems (2005)