LSTRS swMATH ID: 4729 Software Authors: M. Rojas, S. A. Santos, and D. C. Sorensen Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=1326553 Dependencies: Matlab Related Software: GQTPAR; HSL-VF05; ARPACK; GALAHAD; Regularization tools; CUTEst; JDQZ; JDQR; LAPACK; eigs; LSQR; mftoolbox; L-BFGS; SDPT3; SeDuMi; SparseMatrix; CUTEr; Matlab; IRAM; Manopt Cited in: 34 Publications all top 5 Cited by 68 Authors 6 Shen, Chungen 6 Zhang, Lei-Hong 3 Erway, Jennifer B. 3 Yang, Weihong 2 Adachi, Satoru 2 Griffin, Joshua D. 2 Lampe, Jörg 2 Li, Rencang 2 Loli Piccolomini, Elena 2 Marcia, Roummel F. 2 Nakatsukasa, Yuji 2 Pong, Ting Kei 2 Rojas, Marielba 2 Sorensen, Danny C. 2 Voss, Heinrich 1 Apostolopoulou, M. S. 1 Benner, Peter 1 Birgin, Ernesto G. 1 Brezhneva, Olga A. 1 Bruni, Vittoria 1 Brust, Johannes J. 1 Della Cioppa, L. 1 Eldén, Lars 1 Embree, Mark 1 Feng, Jiang 1 Gao, Guohua 1 Gill, Philip E. 1 Gould, Nicholas Ian Mark 1 Gratton, Serge 1 Gürol, Selime 1 Hansen, Per Christian 1 Iwata, Satoru 1 Jia, Xiaojing 1 Jia, Zhongxiao 1 Jiang, Hao 1 Júdice, Joaquim João 1 Kearsley, Anthony José 1 Kelley, Carl T. 1 Kirches, Christian 1 Kolvenbach, Philip 1 Landi, Germana 1 Lass, Oliver 1 Lehoucq, Richard B. 1 Lenders, Felix 1 Li, Qingna 1 Liang, Xin 1 Martin, David R. 1 Martínez, José Mario 1 Omheni, Riadh 1 Potschka, Andreas 1 Qi, Houduo 1 Reichel, Lothar 1 Santos, Sandra Augusta 1 Simoncini, Valeria 1 Sotiropoulos, Dimitris G. 1 Takeda, Akiko 1 Toint, Philippe L. 1 Tret’yakov, Alexey A. 1 Ulbrich, Stefan 1 van Hagen, Paul P. H. 1 Vink, Jeroen C. 1 Vitulano, Domenico 1 Wang, Fa 1 Wells, Terence J. 1 Wolkowicz, Henry 1 Xiu, Naihua 1 Zama, Fabiana 1 Zeng, Liaoyuan all top 5 Cited in 17 Serials 5 SIAM Journal on Optimization 5 Computational Optimization and Applications 5 Optimization Methods & Software 3 SIAM Journal on Scientific Computing 2 BIT 2 SIAM Journal on Matrix Analysis and Applications 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Mathematics and Computers in Simulation 1 Linear Algebra and its Applications 1 Mathematical Programming. Series A. Series B 1 ETNA. Electronic Transactions on Numerical Analysis 1 Taiwanese Journal of Mathematics 1 Computational Geosciences 1 Optimization and Engineering 1 Frontiers of Mathematics in China 1 Optimization Letters all top 5 Cited in 11 Fields 27 Operations research, mathematical programming (90-XX) 26 Numerical analysis (65-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 Partial differential equations (35-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Operator theory (47-XX) 1 History and biography (01-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year