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.

References in zbMATH (referenced in 23 articles )

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  1. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
  2. Lenders, Felix; Kirches, C.; Potschka, A.: \texttttrlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem (2018)
  3. Zhang, Lei-Hong; Shen, Chungen: A nested Lanczos method for the trust-region subproblem (2018)
  4. Zhang, Lei-Hong; Shen, Chungen; Yang, Wei Hong; Júdice, Joaquim J.: A Lanczos method for large-scale extreme Lorentz eigenvalue problems (2018)
  5. Zhang, Leihong; Yang, Weihong; Shen, Chungen; Feng, Jiang: Error bounds of Lanczos approach for trust-region subproblem (2018)
  6. Adachi, Satoru; Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko: Solving the trust-region subproblem by a generalized eigenvalue problem (2017)
  7. Birgin, E. G.; Martínez, J. M.: The use of quadratic regularization with a cubic descent condition for unconstrained optimization (2017)
  8. Brust, Johannes; Erway, Jennifer B.; Marcia, Roummel F.: On solving L-SR1 trust-region subproblems (2017)
  9. Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang: On the generalized Lanczos trust-region method (2017)
  10. 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)
  11. Pong, Ting Kei; Wolkowicz, Henry: The generalized trust region subproblem (2014)
  12. Gratton, Serge; Gürol, Selime; Toint, Philippe L.: Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems (2013)
  13. Landi, G.; Loli Piccolomini, E.: A feasible direction method for image restoration (2012)
  14. Lampe, J.; Rojas, M.; Sorensen, D. C.; Voss, H.: Accelerating the LSTRS algorithm (2011)
  15. Li, Qingna; Qi, Houduo; Xiu, Naihua: Block relaxation and majorization methods for the nearest correlation matrix with factor structure (2011)
  16. Loli Piccolomini, E.; Zama, F.: An iterative algorithm for large size least-squares constrained regularization problems (2011)
  17. Lampe, Jörg; Voss, Heinrich: Solving regularized total least squares problems based on eigenproblems (2010)
  18. Erway, Jennifer B.; Gill, Philip E.; Griffin, Joshua D.: Iterative methods for finding a trust-region step (2009)
  19. Apostolopoulou, M. S.; Sotiropoulos, D. G.; Pintelas, P.: Solving the quadratic trust-region subproblem in a low-memory BFGS framework (2008)
  20. Rojas, Marielba; Santos, Sandra A.; Sorensen, Danny C.: Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization. (2008)

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