On Modified DFP Update for Unconstrained Optimization

Saad Shakir Mahmood; Samira Hassan Shnywer

doi:doi:10.11648/j.ajam.20170501.13

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On Modified DFP Update for Unconstrained Optimization

Saad Shakir Mahmood, Samira Hassan Shnywer

Received: 25 December 2016 Accepted: 9 January 2017 Published: 6 February 2017

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Abstract

In this paper, we propose a new modify of DFP update with a new extended quasi-Newton condition for unconstrained optimization problem so called update. This update is based on a new Zhang Xu condition we show that update preserves the value of determinant of the next Hessian matrix equal to the value of determinant of current Hessian matrix theoretically and practically. Global convergence of the modify is established. Local and super linearly convergence are obtained for the proposed method. Numerical results are given to compare a performance of the modify method with the standard DFP method on same function is selected.

DOI	10.11648/j.ajam.20170501.13
Published in	American Journal of Applied Mathematics (Volume 5, Issue 1, February 2017)
Page(s)	19-30
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Quasi-Newton Equation, the DFP Updating Formula, Global Convergence and Super Linearly Convergence

References

[1]	Al-Bayati, A., (1991), A new family of self-scaling variable metric Algorithms for unconstraint optimization, Journal of Educ. and Sci., Iraq, Vol. 12, pp. 25-54.
[2]	Dennis J. E., More J., (1974), "A characterization of super linear Convergence and its application to quasi-Newton methods Math and Computation 28 (6) 549-60.
[3]	F. Freudenstein and B. Roth,(1962), Numerical solution of system of nonlinear equations, Journal of ACM, Vol. 10, No. 4, pp. 550-556.
[4]	H. H. Rosen brock, (1960), An automatic method for finding the greatest least value of a function, Computer Journal, Vol. 3, No. 3, pp. 175-184.
[5]	J. E. Dennis, Jr. and Robert B. Schnabel, (1996), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Classics in Applied Mathematics.
[6]	Oren, S. S (1973), Self-scaling Variable Metric Algorithms without line search for Unconstrained minimization. Mathematics of computation, 27: 873-885.
[7]	Saad S. Mahmood, (2011), α-BFGS update for Unconstrained Opt-imization, Journal of college of Education, No. 1, Almustansiriya University.
[8]	Todd M. J., (1984), Quasi-Newton updates in abstract spaces, SIAM Review, 26: 367-377.
[9]	W. Sun and Y. Yuan, (2006), "Optimization Theory and Method: Nonlinear Programing", Vol. 1 of Springer optimization and its Applications, Springer, New York, NY, USA.
[10]	Yuan, Y., (1990), On a Modified Algorithm for Unconstrained Optimization, Computing Center, Academia Sinica, Beijing, China.

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Saad Shakir Mahmood, Samira Hassan Shnywer. (2017). On Modified DFP Update for Unconstrained Optimization. American Journal of Applied Mathematics, 5(1), 19-30. https://doi.org/10.11648/j.ajam.20170501.13

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ACS Style

Saad Shakir Mahmood; Samira Hassan Shnywer. On Modified DFP Update for Unconstrained Optimization. Am. J. Appl. Math. 2017, 5(1), 19-30. doi: 10.11648/j.ajam.20170501.13

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AMA Style

Saad Shakir Mahmood, Samira Hassan Shnywer. On Modified DFP Update for Unconstrained Optimization. Am J Appl Math. 2017;5(1):19-30. doi: 10.11648/j.ajam.20170501.13

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@article{10.11648/j.ajam.20170501.13,
  author = {Saad Shakir Mahmood and Samira Hassan Shnywer},
  title = {On Modified DFP Update for Unconstrained Optimization},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {19-30},
  doi = {10.11648/j.ajam.20170501.13},
  url = {https://doi.org/10.11648/j.ajam.20170501.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170501.13},
  abstract = {In this paper, we propose a new modify of DFP update with a new extended quasi-Newton condition for unconstrained optimization problem so called  update. This update is based on a new Zhang Xu condition we show that  update preserves the value of determinant of the next Hessian matrix equal to the value of determinant of current Hessian matrix theoretically and practically. Global convergence of the modify is established. Local and super linearly convergence are obtained for the proposed method. Numerical results are given to compare a performance of the modify  method with the standard DFP method on same function is selected.},
 year = {2017}
}

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TY  - JOUR
T1  - On Modified DFP Update for Unconstrained Optimization
AU  - Saad Shakir Mahmood
AU  - Samira Hassan Shnywer
Y1  - 2017/02/06
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.13
DO  - 10.11648/j.ajam.20170501.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 19
EP  - 30
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170501.13
AB  - In this paper, we propose a new modify of DFP update with a new extended quasi-Newton condition for unconstrained optimization problem so called  update. This update is based on a new Zhang Xu condition we show that  update preserves the value of determinant of the next Hessian matrix equal to the value of determinant of current Hessian matrix theoretically and practically. Global convergence of the modify is established. Local and super linearly convergence are obtained for the proposed method. Numerical results are given to compare a performance of the modify  method with the standard DFP method on same function is selected.
VL  - 5
IS  - 1
ER  -

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Author Information

Saad Shakir Mahmood

Department of Mathematics, College of Education, Almustansiryah University, Baghdad, Iraq
Samira Hassan Shnywer

Department of Mathematics, College of Education, Almustansiryah University, Baghdad, Iraq

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APA Style

Saad Shakir Mahmood, Samira Hassan Shnywer. (2017). On Modified DFP Update for Unconstrained Optimization. American Journal of Applied Mathematics, 5(1), 19-30. https://doi.org/10.11648/j.ajam.20170501.13

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ACS Style

Saad Shakir Mahmood; Samira Hassan Shnywer. On Modified DFP Update for Unconstrained Optimization. Am. J. Appl. Math. 2017, 5(1), 19-30. doi: 10.11648/j.ajam.20170501.13

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AMA Style

Saad Shakir Mahmood, Samira Hassan Shnywer. On Modified DFP Update for Unconstrained Optimization. Am J Appl Math. 2017;5(1):19-30. doi: 10.11648/j.ajam.20170501.13

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@article{10.11648/j.ajam.20170501.13,
  author = {Saad Shakir Mahmood and Samira Hassan Shnywer},
  title = {On Modified DFP Update for Unconstrained Optimization},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {1},
  pages = {19-30},
  doi = {10.11648/j.ajam.20170501.13},
  url = {https://doi.org/10.11648/j.ajam.20170501.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170501.13},
  abstract = {In this paper, we propose a new modify of DFP update with a new extended quasi-Newton condition for unconstrained optimization problem so called  update. This update is based on a new Zhang Xu condition we show that  update preserves the value of determinant of the next Hessian matrix equal to the value of determinant of current Hessian matrix theoretically and practically. Global convergence of the modify is established. Local and super linearly convergence are obtained for the proposed method. Numerical results are given to compare a performance of the modify  method with the standard DFP method on same function is selected.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - On Modified DFP Update for Unconstrained Optimization
AU  - Saad Shakir Mahmood
AU  - Samira Hassan Shnywer
Y1  - 2017/02/06
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170501.13
DO  - 10.11648/j.ajam.20170501.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 19
EP  - 30
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170501.13
AB  - In this paper, we propose a new modify of DFP update with a new extended quasi-Newton condition for unconstrained optimization problem so called  update. This update is based on a new Zhang Xu condition we show that  update preserves the value of determinant of the next Hessian matrix equal to the value of determinant of current Hessian matrix theoretically and practically. Global convergence of the modify is established. Local and super linearly convergence are obtained for the proposed method. Numerical results are given to compare a performance of the modify  method with the standard DFP method on same function is selected.
VL  - 5
IS  - 1
ER  -

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