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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  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)
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  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)
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  18. Haber, Eldad; Horesh, Raya; Modersitzki, Jan: Numerical optimization for constrained image registration (2010)
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  20. Lin, Lu: Alternative gradient algorithms with applications to nonnegative matrix factorizations (2010)