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Journal of Applied Mathematics
Volume 2013, Article ID 523476, 8 pages
http://dx.doi.org/10.1155/2013/523476
Research Article

Diagonal Hessian Approximation for Limited Memory Quasi-Newton via Variational Principle

1Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematics, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 23 July 2013; Revised 21 October 2013; Accepted 19 November 2013

Academic Editor: Martin Weiser

Copyright © 2013 Siti Mahani Marjugi and Wah June Leong. 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. F. Modarres, M. A. Hassan, and W. J. Leong, “Improved Hessian approximation with modified secant equations for symmetric rank-one method,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2423–2431, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. J. Moré, B. S. Garbow, and K. E. Hillstrom, “Testing unconstrained optimization software,” ACM Transactions on Mathematical Software, vol. 7, no. 1, pp. 17–41, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. I. Bongartz, A. R. Conn, N. Gould, and Ph. L. Toint, “CUTE: constrained and unconstrained testing environment,” ACM Transactions on Mathematical Software, vol. 21, no. 1, pp. 123–160, 1995. View at Publisher · View at Google Scholar · View at Scopus
  4. Ph. L. Toint, “Test problems for partially separable optimization and results for the routine PSPMIN,” Tech. Rep. 83/4, Department of Mathematics, University of Namur, Brussels, Belgium, 1983. View at Google Scholar
  5. M. Zhu, J. L. Nazareth, and H. Wolkowicz, “The Quasi-Cauchy relation and diagonal updating,” SIAM Journal on Optimization, vol. 9, no. 4, pp. 1192–1204, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Farid and W. J. Leong, “An improved multi-step gradient-type method for large scale optimization,” Computers & Mathematics with Applications, vol. 61, no. 11, pp. 3312–3318, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, New York, NY, USA, 1983.
  8. J. C. Gilbert and C. Lemaréchal, “Some numerical experiments with variable-storage quasi-Newton algorithms,” Mathematical Programming, vol. 45, no. 1–3, pp. 407–435, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Mathematical Programming, vol. 45, no. 1–3, pp. 503–528, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. 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 Zentralblatt MATH · View at MathSciNet