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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 610612, 8 pages
http://dx.doi.org/10.1155/2014/610612
Research Article

A Novel Self-Adaptive Trust Region Algorithm for Unconstrained Optimization

School of Mathematics and Statistics, Beihua University, Jilin 132013, China

Received 28 August 2013; Revised 18 March 2014; Accepted 19 March 2014; Published 15 April 2014

Academic Editor: Kazutake Komori

Copyright © 2014 Yunlong Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods, MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM); Mathematical Programming Society (MPS), Philadelphia, Pa, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  2. J. M. B. Walmag and E. J. M. Delhez, “A note on trust-region radius update,” SIAM Journal on Optimization, vol. 16, no. 2, pp. 548–562, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. Sartenaer, “Automatic determination of an initial trust region in nonlinear programming,” SIAM Journal on Scientific Computing, vol. 18, no. 6, pp. 1788–1803, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  4. X. Zhang, J. Zhang, and L. Liao, “An adaptive trust region method and its convergence,” Science in China A, vol. 45, no. 5, pp. 620–631, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  5. X. S. Zhang, “Trust region method in neural network,” Acta Mathematicae Applicatae Sinica, vol. 12, pp. 1–10, 1996. View at Google Scholar
  6. Z.-J. Shi and J.-H. Guo, “A new trust region method for unconstrained optimization,” Journal of Computational and Applied Mathematics, vol. 213, no. 2, pp. 509–520, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. Fu, W. Sun, and R. J. B. de Sampaio, “An adaptive approach of conic trust-region method for unconstrained optimization problems,” Journal of Applied Mathematics & Computing, vol. 19, no. 1-2, pp. 165–177, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Z. Sang and Q. Sun, “A self-adaptive trust region method with line search based on a simple subproblem model,” Journal of Computational and Applied Mathematics, vol. 232, no. 2, pp. 514–522, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Z. Yu and Q. Li, “A self-adaptive trust region method for the extended linear complementarity problems,” Applications of Mathematics, vol. 54, no. 1, pp. 53–65, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. N. I. M. Gould, D. Orban, A. Sartenaer, and P. L. Toint, “Sensitivity of trust-region algorithms to their parameters,” 4OR. A Quarterly Journal of Operations Research, vol. 3, no. 3, pp. 227–241, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J.-L. Zhang and X.-S. Zhang, “A nonmonotone adaptive trust region method and its convergence,” Computers & Mathematics with Applications, vol. 45, no. 10-11, pp. 1469–1477, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Fu and W. Sun, “Nonmonotone adaptive trust-region method for unconstrained optimization problems,” Applied Mathematics and Computation, vol. 163, no. 1, pp. 489–504, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Zhang, K. Zhang, and S. Qu, “A nonmonotone adaptive trust region method for unconstrained optimization based on conic model,” Applied Mathematics and Computation, vol. 217, no. 8, pp. 4265–4273, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Ahookhosh and K. Amini, “A nonmonotone trust region method with adaptive radius for unconstrained optimization problems,” Computers & Mathematics with Applications, vol. 60, no. 3, pp. 411–422, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  15. N. Andrei, “An unconstrained optimization test functions collection,” Advanced Modeling and Optimization, vol. 10, no. 1, pp. 147–161, 2008. View at Google Scholar · View at MathSciNet
  16. Z. Shi and S. Wang, “Nonmonotone adaptive trust region method,” European Journal of Operational Research, vol. 208, no. 1, pp. 28–36, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z. Sang and Q. Sun, “A new non-monotone self-adaptive trust region method for unconstrained optimization,” Journal of Applied Mathematics and Computing, vol. 35, no. 1-2, pp. 53–62, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Z. Cui and B. Wu, “A new modified nonmonotone adaptive trust region method for unconstrained optimization,” Computational Optimization and Applications, vol. 53, no. 3, pp. 795–806, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. L. Hei, “A self-adaptive trust region algorithm,” Journal of Computational Mathematics, vol. 21, no. 2, pp. 229–236, 2003. View at Google Scholar · View at MathSciNet
  20. J. Nocedal and S. T. Wright, Numerical Optimization, Springer, Berlin, Germany, 2000.
  21. W. Sun and Y.-X. Yuan, Optimization Theory and Methods, Nonlinear programming, vol. 1 of Springer Optimization and Its Applications, Springer, New York, NY, USA, 2006. View at MathSciNet
  22. J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “Testing unconstrained optimization software,” Association for Computing Machinery. Transactions on Mathematical Software, vol. 7, no. 1, pp. 17–41, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  23. N. I. M. Gould, D. Orban, and P. L. Toint, “GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization,” Association for Computing Machinery. Transactions on Mathematical Software, vol. 29, no. 4, pp. 353–372, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  24. E. D. Dolan and J. J. Moré, “Benchmarking optimization software with performance profiles,” Mathematical Programming, vol. 9, pp. 1201–1213, 2002. View at Google Scholar