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On the Global Convergence of the PERRY-SHANNO Method for Nonconvex Unconstrained Optimization Problems

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DOI: 10.4236/am.2011.23037    3,917 Downloads   7,413 Views   Citations

ABSTRACT

In this paper, we prove the global convergence of the Perry-Shanno’s memoryless quasi-Newton (PSMQN) method with a new inexact line search when applied to nonconvex unconstrained minimization problems. Preliminary numerical results show that the PSMQN with the particularly line search conditions are very promising.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. Huang, Q. Wu and G. Yuan, "On the Global Convergence of the PERRY-SHANNO Method for Nonconvex Unconstrained Optimization Problems," Applied Mathematics, Vol. 2 No. 3, 2011, pp. 315-320. doi: 10.4236/am.2011.23037.

References

[1] J. M. Perry, “A Class of Conjugate Algorithms with a Two Step Variable Metric Memory,” Discussion Paper 269, Northwestern University, 1977.
[2] D. F. Shanno, “On the Convergence of a New Conjugate Gradient Algorithm,” SIAM Journal on Numerical Analysis, Vol. 15, No. 6, 1978, pp. 1247-1257. doi:10.1137/0715085
[3] J. Y. Han, G. H. Liu and H. X. Yin, “Convergence of Perry and Shanno’s Memoryless Quasi-Newton Method of Nonconvex Optimization Problems,” On Transactions, Vol. 1, No. 3, 1997, pp. 22-28.
[4] J. J. More, B. S. Garbow and K. E. Hillstrome, “Testing Unconstrained Optimization Software,” ACM Transactions on Mathematical Software, Vol. 7, No. 1, 1981, pp. 17-41. doi:10.1145/355934.355936
[5] A. Griewank, “On Automatic Differentiation,” Kluwer Academic Publishers, Norwell, 1989.
[6] Y. Dai and Q. Ni, “Testing Different Conjugate Gradient Methods for Large-Scale Unconstrained Optimization,” Journal of Computational Mathematics, Vol. 21, No. 3, 2003, pp. 311-320.

  
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