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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 478407, 6 pages
A Newton-Like Trust Region Method for Large-Scale Unconstrained Nonconvex Minimization
School of Mathematics and Statistics, Beihua University, Jilin 132013, China
Received 8 June 2013; Accepted 4 September 2013
Academic Editor: Bo-Qing Dong
Copyright © 2013 Yang Weiwei 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.
- M. J. D. Powell, “A new algorithm for unconstrained optimization,” in Nonlinear Programming, J. B. Rosen, O. L. Mangasarian, and K. Ritter, Eds., pp. 31–65, Academic Press, New York, NY, USA, 1970.
- J. Nocedal and Y.-X. Yuan, “Combining trust region and line search techniques,” in Advances in Nonlinear Programming, Y. Yuan, Ed., vol. 14, pp. 153–175, Kluwer Academic, Dordrecht, The Netherlands, 1998.
- J. Nocedal and S. J. Wright, Numerical Optimization, Springer, New York, NY, USA, 1999.
- A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 2000.
- H. P. Wu and Q. Ni, “A new trust region algorithm with a conic model,” Numerical Mathematics, vol. 30, no. 1, pp. 57–67, 2008.
- Ph. L. Toint, “Global convergence of a class of trust-region methods for nonconvex minimization in Hilbert space,” IMA Journal of Numerical Analysis, vol. 8, no. 2, pp. 231–252, 1988.
- M. J. D. Powell and Y. Yuan, “A trust region algorithm for equality constrained optimization,” Mathematical Programming, vol. 49, no. 2, pp. 189–211, 1990.
- D.-H. Li and M. Fukushima, “A modified BFGS method and its global convergence in nonconvex minimization,” Journal of Computational and Applied Mathematics, vol. 129, no. 1-2, pp. 15–35, 2001.
- Y. Nesterov and B. T. Polyak, “Cubic regularization of Newton method and its global performance,” Mathematical Programming, vol. 108, no. 1, pp. 177–205, 2006.
- Q. Guo and J.-G. Liu, “Global convergence of a modified BFGS-type method for unconstrained non-convex minimization,” Journal of Applied Mathematics & Computing, vol. 24, no. 1-2, pp. 325–331, 2007.
- S. Gratton, A. Sartenaer, and P. L. Toint, “Recursive trust-region methods for multiscale nonlinear optimization,” SIAM Journal on Optimization, vol. 19, no. 1, pp. 414–444, 2008.
- C. Cartis, N. I. M. Gould, and P. L. Toint, “On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization problems,” SIAM Journal on Optimization, vol. 20, no. 6, pp. 2833–2852, 2010.
- C. Cartis, N. I. M. Gould, and P. L. Toint, “Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results,” Mathematical Programming, vol. 127, no. 2, pp. 245–295, 2011.
- D. Xue, W. Sun, and H. He, “A structured trust region method for nonconvex programming with separable structure,” Numerical Algebra, Control and Optimization, vol. 3, no. 2, pp. 283–293, 2013.
- J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Mathematics of Computation, vol. 35, no. 151, pp. 773–782, 1980.
- D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Mathematical Programming, vol. 45, no. 3, pp. 503–528, 1989.
- R. H. Byrd, J. Nocedal, and R. B. Schnabel, “Representations of quasi-Newton matrices and their use in limited memory methods,” Mathematical Programming, vol. 63, no. 2, pp. 129–156, 1994.
- C. Xu and J. Zhang, “A survey of quasi-Newton equations and quasi-Newton methods for optimization,” Annals of Operations Research, vol. 103, pp. 213–234, 2001.
- Y. T. Yang and C. X. Xu, “A compact limited memory method for large scale unconstrained optimization,” European Journal of Operational Research, vol. 180, no. 1, pp. 48–56, 2007.
- Q. Ni and Y. Yuan, “A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization,” Mathematics of Computation, vol. 66, no. 220, pp. 1509–1520, 1997.
- O. P. Burdakov, J. M. Martínez, and E. A. Pilotta, “A limited-memory multipoint symmetric secant method for bound constrained optimization,” Annals of Operations Research, vol. 117, no. 1–4, pp. 51–70, 2002.
- Z. H. Wang, “A limited memory trust region method for unconstrained optimization and its implementation,” Mathematica Numerica Sinica, vol. 27, no. 4, pp. 395–404, 2005.
- P. E. Gill, W. Murray, and M. A. Saunders, “SNOPT: an SQP algorithm for large-scale constrained optimization,” SIAM Review, vol. 47, no. 1, pp. 99–131, 2005.
- H. Liu and Q. Ni, “New limited-memory symmetric secant rank one algorithm for large-scale unconstrained optimization,” Transactions of Naniing University of Aeronautics and Astronautics, vol. 25, no. 3, pp. 235–239, 2008.
- J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “Testing unconstrained optimization software,” Association for Computing Machinery, vol. 7, no. 1, pp. 17–41, 1981.
- 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, vol. 29, no. 4, pp. 353–372, 2003.
- H. Y. Benson, “Cute models,” http://orfe.princeton.edu/~rvdb/ampl/nlmodels/cute/.