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 32 articles )
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Sorted by year (- Lampe, Jörg; Voss, Heinrich: A survey on variational characterizations for nonlinear eigenvalue problems (2022)
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- Erway, Jennifer B.; Griffin, Joshua; Marcia, Roummel F.; Omheni, Riadh: Trust-region algorithms for training responses: machine learning methods using indefinite Hessian approximations (2020)
- Gao, Guohua; Jiang, Hao; Vink, Jeroen C.; van Hagen, Paul P. H.; Wells, Terence J.: Performance enhancement of Gauss-Newton trust-region solver for distributed Gauss-Newton optimization method (2020)
- Gould, Nicholas I. M.; Simoncini, Valeria: Error estimates for iterative algorithms for minimizing regularized quadratic subproblems (2020)
- Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
- Kolvenbach, Philip; Lass, Oliver; Ulbrich, Stefan: An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty (2018)
- Lenders, Felix; Kirches, C.; Potschka, A.: \texttttrlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem (2018)
- Zhang, Lei-Hong; Shen, Chungen: A nested Lanczos method for the trust-region subproblem (2018)
- Zhang, Lei-Hong; Shen, Chungen; Yang, Wei Hong; Júdice, Joaquim J.: A Lanczos method for large-scale extreme Lorentz eigenvalue problems (2018)
- Zhang, Leihong; Yang, Weihong; Shen, Chungen; Feng, Jiang: Error bounds of Lanczos approach for trust-region subproblem (2018)
- Adachi, Satoru; Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko: Solving the trust-region subproblem by a generalized eigenvalue problem (2017)
- Birgin, E. G.; Martínez, J. M.: The use of quadratic regularization with a cubic descent condition for unconstrained optimization (2017)
- Brust, Johannes; Erway, Jennifer B.; Marcia, Roummel F.: On solving L-SR1 trust-region subproblems (2017)
- Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang: On the generalized Lanczos trust-region method (2017)
- 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)
- Martin, David R.; Reichel, Lothar: Minimization of functionals on the solution of a large-scale discrete ill-posed problem (2013)