TRON

TRON is a trust region Newton method for the solution of large bound-constrained optimization problems. TRON uses a gradient projection method to generate a Cauchy step, a preconditioned conjugate gradient method with an incomplete Cholesky factorization to generate a direction, and a projected search to compute the step. The use of projected searches, in particular, allows TRON to examine faces of the feasible set by generating a small number of minor iterates, even for problems with a large number of variables. As a result TRON is remarkably efficient at solving large bound-constrained optimization problems.


References in zbMATH (referenced in 100 articles , 1 standard article )

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  1. De Simone, V.; di Serafino, D.: A matrix-free approach to build band preconditioners for large-scale bound-constrained optimization (2014)
  2. Le Thi, Hoai An; Huynh Van Ngai; Dinh, Tao Pham; Vaz, A. Ismael F.; Vicente, L. N.: Globally convergent DC trust-region methods (2014)
  3. Peng, Jing-Jing; Peng, Zhen-Yun: Least squares symmetric solutions to a matrix equation with a matrix inequality constraint (2014)
  4. Barrera Sánchez, P.; Cortés, J. J.; González Flores, G.: Harmonic hexahedral structured grid generation (2013)
  5. Byrd, Richard H.; Chin, Gillian M.; Nocedal, Jorge; Wu, Yuchen: Sample size selection in optimization methods for machine learning (2012)
  6. Cheng, Wanyou; Li, Donghui: An active set modified Polak-Ribiére-Polyak method for large-scale nonlinear bound constrained optimization (2012)
  7. Haber, Eldad; Magnant, Zhuojun; Lucero, Christian; Tenorio, Luis: Numerical methods for (A)-optimal designs with a sparsity constraint for ill-posed inverse problems (2012)
  8. Lantoine, Gregory; Russell, Ryan P.: A hybrid differential dynamic programming algorithm for constrained optimal control problems. I: Theory (2012)
  9. Bonettini, Silvia: Inexact block coordinate descent methods with application to non-negative matrix factorization (2011)
  10. Byrd, Richard H.; Waltz, Richard A.: An active-set algorithm for nonlinear programming using parametric linear programming (2011)
  11. Gratton, Serge; Toint, Philippe L.; Tröltzsch, Anke: An active-set trust-region method for derivative-free nonlinear bound-constrained optimization (2011)
  12. Lin, Lu; Liu, Zhong-Yun: An alternating projected gradient algorithm for nonnegative matrix factorization (2011)
  13. Sun, Li; He, Guoping; Wang, Yongli; Zhou, Changyin: An accurate active set Newton algorithm for large scale bound constrained optimization. (2011)
  14. Xiao, Yun-Hai; Hu, Qing-Jie; Wei, Zengxin: Modified active set projected spectral gradient method for bound constrained optimization (2011)
  15. Yuan, Gonglin; Lu, Xiwen: An active set limited memory BFGS algorithm for bound constrained optimization (2011)
  16. Guerrero-García, Pablo; Santos-Palomo, Ángel: A sparse counterpart of Reichel and Gragg’s package QRUP (2010)
  17. Haber, E.; Horesh, L.; Tenorio, L.: Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems (2010)
  18. Haber, Eldad; Horesh, Raya; Modersitzki, Jan: Numerical optimization for constrained image registration (2010)
  19. Kim, Dongmin; Sra, Suvrit; Dhillon, Inderjit S.: Tackling box-constrained optimization via a new projected quasi-Newton approach (2010)
  20. Lin, Lu: Alternative gradient algorithms with applications to nonnegative matrix factorizations (2010)