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 94 articles , 1 standard article )

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  1. Belachew, Melisew Tefera; Gillis, Nicolas: Solving the maximum clique problem with symmetric rank-one non-negative matrix approximation (2017)
  2. Caudillo-Mata, L.A.; Haber, E.; Heagy, L.J.; Schwarzbach, C.: A framework for the upscaling of the electrical conductivity in the quasi-static Maxwell’s equations (2017)
  3. Chen, Tianyi; Curtis, Frank E.; Robinson, Daniel P.: A reduced-space algorithm for minimizing $\ell_1$-regularized convex functions (2017)
  4. Cristofari, Andrea; De Santis, Marianna; Lucidi, Stefano; Rinaldi, Francesco: A two-stage active-set algorithm for bound-constrained optimization (2017)
  5. Stiegelmeier, Elenice W.; Oliveira, Vilma A.; Silva, Geraldo N.; Karam, Décio: Optimal weed population control using nonlinear programming (2017)
  6. Arreckx, Sylvain; Lambe, Andrew; Martins, Joaquim R.R.A.; Orban, Dominique: A matrix-free augmented Lagrangian algorithm with application to large-scale structural design optimization (2016)
  7. Dong, Jun-Liang; Gao, Junbin; Ju, Fujiao; Shen, Jinghua: Modulus methods for nonnegatively constrained image restoration (2016)
  8. Hager, William W.; Zhang, Hongchao: An active set algorithm for nonlinear optimization with polyhedral constraints (2016)
  9. Rahpeymaii, Farzad; Kimiaei, Morteza; Bagheri, Alireza: A limited memory quasi-Newton trust-region method for box constrained optimization (2016)
  10. Bui-Thanh, Tan; Ghattas, Omar: A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors (2015)
  11. Peyghami, M.Reza; Tarzanagh, D.Ataee: A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems (2015)
  12. Tarzanagh, D.Ataee; Peyghami, M.Reza; Bastin, F.: A new nonmonotone adaptive retrospective trust region method for unconstrained optimization problems (2015)
  13. Yuan, Gonglin; Wei, Zengxin; Zhang, Maojun: An active-set projected trust region algorithm for box constrained optimization problems (2015)
  14. Cheng, Wanyou; Chen, Zixin; Li, Dong-hui: An active set truncated Newton method for large-scale bound constrained optimization (2014)
  15. Cheng, Wanyou; Liu, Qunfeng; Li, Donghui: An accurate active set conjugate gradient algorithm with project search for bound constrained optimization (2014)
  16. De Simone, V.; di Serafino, D.: A matrix-free approach to build band preconditioners for large-scale bound-constrained optimization (2014)
  17. Le Thi, Hoai An; Huynh Van Ngai; Dinh, Tao Pham; Vaz, A.Ismael F.; Vicente, L.N.: Globally convergent DC trust-region methods (2014)
  18. Peng, Jing-Jing; Peng, Zhen-Yun: Least squares symmetric solutions to a matrix equation with a matrix inequality constraint (2014)
  19. Byrd, Richard H.; Chin, Gillian M.; Nocedal, Jorge; Wu, Yuchen: Sample size selection in optimization methods for machine learning (2012)
  20. Cheng, Wanyou; Li, Donghui: An active set modified Polak-Ribiére-Polyak method for large-scale nonlinear bound constrained optimization (2012)

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