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.

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  1. Dong, Jun-Liang; Gao, Junbin; Ju, Fujiao; Shen, Jinghua: Modulus methods for nonnegatively constrained image restoration (2016)
  2. Hager, William W.; Zhang, Hongchao: An active set algorithm for nonlinear optimization with polyhedral constraints (2016)
  3. Rahpeymaii, Farzad; Kimiaei, Morteza; Bagheri, Alireza: A limited memory quasi-Newton trust-region method for box constrained optimization (2016)
  4. Peyghami, M.Reza; Tarzanagh, D.Ataee: A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems (2015)
  5. Tarzanagh, D.Ataee; Peyghami, M.Reza; Bastin, F.: A new nonmonotone adaptive retrospective trust region method for unconstrained optimization problems (2015)
  6. Yuan, Gonglin; Wei, Zengxin; Zhang, Maojun: An active-set projected trust region algorithm for box constrained optimization problems (2015)
  7. Cheng, Wanyou; Chen, Zixin; Li, Dong-hui: An active set truncated Newton method for large-scale bound constrained optimization (2014)
  8. Cheng, Wanyou; Liu, Qunfeng; Li, Donghui: An accurate active set conjugate gradient algorithm with project search for bound constrained optimization (2014)
  9. De Simone, V.; di Serafino, D.: A matrix-free approach to build band preconditioners for large-scale bound-constrained optimization (2014)
  10. Le Thi, Hoai An; Huynh Van Ngai; Dinh, Tao Pham; Vaz, A.Ismael F.; Vicente, L.N.: Globally convergent DC trust-region methods (2014)
  11. Peng, Jing-Jing; Peng, Zhen-Yun: Least squares symmetric solutions to a matrix equation with a matrix inequality constraint (2014)
  12. Byrd, Richard H.; Chin, Gillian M.; Nocedal, Jorge; Wu, Yuchen: Sample size selection in optimization methods for machine learning (2012)
  13. Cheng, Wanyou; Li, Donghui: An active set modified Polak-Ribiére-Polyak method for large-scale nonlinear bound constrained optimization (2012)
  14. Haber, Eldad; Magnant, Zhuojun; Lucero, Christian; Tenorio, Luis: Numerical methods for $A$-optimal designs with a sparsity constraint for ill-posed inverse problems (2012)
  15. Lantoine, Gregory; Russell, Ryan P.: A hybrid differential dynamic programming algorithm for constrained optimal control problems. I: Theory (2012)
  16. Bonettini, Silvia: Inexact block coordinate descent methods with application to non-negative matrix factorization (2011)
  17. Byrd, Richard H.; Waltz, Richard A.: An active-set algorithm for nonlinear programming using parametric linear programming (2011)
  18. Gratton, Serge; Toint, Philippe L.; Tröltzsch, Anke: An active-set trust-region method for derivative-free nonlinear bound-constrained optimization (2011)
  19. Lin, Lu; Liu, Zhong-Yun: An alternating projected gradient algorithm for nonnegative matrix factorization (2011)
  20. Sun, Li; He, Guoping; Wang, Yongli; Zhou, Changyin: An accurate active set Newton algorithm for large scale bound constrained optimization. (2011)

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