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. Shen, Chungen; Fan, Changxing; Wang, Yunlong; Xue, Wenjuan: Limited memory BFGS algorithm for the matrix approximation problem in Frobenius norm (2020)
  2. Zhang, Chao; Chen, Xiaojun: A smoothing active set method for linearly constrained non-Lipschitz nonconvex optimization (2020)
  3. Austin, Anthony P.; Di, Zichao; Leyffer, Sven; Wild, Stefan M.: Simultaneous sensing error recovery and tomographic inversion using an optimization-based approach (2019)
  4. Dahito, Marie-Ange; Orban, Dominique: The conjugate residual method in linesearch and trust-region methods (2019)
  5. Wang, Guoqiang; Yu, Bo: PAL-Hom method for QP and an application to LP (2019)
  6. Barbero, Álvaro; Sra, Suvrit: Modular proximal optimization for multidimensional total-variation regularization (2018)
  7. Bottou, Léon; Curtis, Frank E.; Nocedal, Jorge: Optimization methods for large-scale machine learning (2018)
  8. Caliciotti, Andrea; Fasano, Giovanni; Nash, Stephen G.; Roma, Massimo: An adaptive truncation criterion, for linesearch-based truncated Newton methods in large scale nonconvex optimization (2018)
  9. Piccialli, Veronica; Sciandrone, Marco: Nonlinear optimization and support vector machines (2018)
  10. Yan, Xihong; Wang, Kai; He, Hongjin: On the convergence rate of scaled gradient projection method (2018)
  11. Ahookhosh, Masoud; Neumaier, Arnold: An optimal subgradient algorithm for large-scale bound-constrained convex optimization (2017)
  12. Belachew, Melisew Tefera; Gillis, Nicolas: Solving the maximum clique problem with symmetric rank-one non-negative matrix approximation (2017)
  13. 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)
  14. Chang, J.; Nakshatrala, K. B.: Variational inequality approach to enforcing the non-negative constraint for advection-diffusion equations (2017)
  15. Chen, Tianyi; Curtis, Frank E.; Robinson, Daniel P.: A reduced-space algorithm for minimizing (\ell_1)-regularized convex functions (2017)
  16. Cristofari, Andrea; De Santis, Marianna; Lucidi, Stefano; Rinaldi, Francesco: A two-stage active-set algorithm for bound-constrained optimization (2017)
  17. Stiegelmeier, Elenice W.; Oliveira, Vilma A.; Silva, Geraldo N.; Karam, Décio: Optimal weed population control using nonlinear programming (2017)
  18. 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)
  19. Dong, Jun-Liang; Gao, Junbin; Ju, Fujiao; Shen, Jinghua: Modulus methods for nonnegatively constrained image restoration (2016)
  20. Hager, William W.; Zhang, Hongchao: An active set algorithm for nonlinear optimization with polyhedral constraints (2016)

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