On Quasi-Newton Method for Solving Unconstrained Optimization Problems

Felix Makanjuola Aderibigbe; Kayode James Adebayo; Adejoke O. Dele-Rotimi

doi:doi:10.11648/j.ajam.20150302.13

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On Quasi-Newton Method for Solving Unconstrained Optimization Problems

Felix Makanjuola Aderibigbe, Kayode James Adebayo, Adejoke O. Dele-Rotimi

Published in American Journal of Applied Mathematics (Volume 3, Issue 2)

Received: 25 December 2014 Accepted: 14 February 2015 Published: 26 February 2015

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Abstract

This paper discusses the use of quasi-Newton method algorithm employed in solving unconstrained optimization problems. The method is aimed at circumventing the computational rigours undergone using the Newton’s method.The Quasi –Newton method algorithm was tested on some benced mark problems with the results compared with the Conjugate Gradient Method. The results gotten using the Quasi-Newton Method compared favourably with results of existing CGM algorithm.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.ajam.20150302.13
Page(s)	47-50
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), 2015. Published by Science Publishing Group

Keywords

Optimization Problems, Conjugate Gradient Method, Control Operator

References

[1]	BROYDEN, C.G. (1965). “A Class of Methods for Solving Nonlinear Simultaneous Equations”. Math. Comp., 19,pp. 577-593.
[2]	DAVIDON, W.C. (1959).”Variable Metric Method for Minimization”, Rep.ANL-5990 Rev, Argonne National Laboratories, Argonne, I11
[3]	DENNIS, J.E. JR and MORÉ,J.J. (1977). “Quasi Newton Methods, Motivation and Theory” SIAMReview 19(1), pp 46-89
[4]	FLETCHER, R., and POWELL, M.J.D.,(1963), “A rapidly Convergent Descent Method for Minimization.” Comput. J.,6, pp 163-168.
[5]	HESTENES, M. R., and STIEFEL, E., (1952), “Method of Conjugate Gradients for solving Linear Systems,” J. Res. Nat. Bur. Standards 49, pp 409- 436.
[6]	IBIEJUGBA, M. A. and ONUMANYI, P., (1984), “A Control Operator and Someof itsApplications,” Journal of Mathematical Analysis and Applications, Vol.103,No.1, pp 31-47.
[7]	IGOR, G., STEPHEN, G. N. and ARIELA, S., (2009), Linear and NonlinearOptimization, 2nd edition. George Mason University, Fairfax, Virginia, SIAM,Philadelphia.
[8]	Jorge NOCEDAL and Stephen J. WRIGHT. (2006), Numerical Optimization. 2nd edition.Springer-Verlag, New York.
[9]	LAWRENCE, Hasdorff, (1976), Gradient Optimization and Nonlinear Control. J.Wileyand Sons, New York.
[10]	RAO, S. S., (1978),Optimization Theory and Applications, Wiley and Sons. NewYork.
[11]	THOMAS, F. E., and DAVID, M. H., (2001), Optimization of Chemical Processes, McGraw Hill Comp.

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APA Style

Felix Makanjuola Aderibigbe, Kayode James Adebayo, Adejoke O. Dele-Rotimi. (2015). On Quasi-Newton Method for Solving Unconstrained Optimization Problems. American Journal of Applied Mathematics, 3(2), 47-50. https://doi.org/10.11648/j.ajam.20150302.13

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ACS Style

Felix Makanjuola Aderibigbe; Kayode James Adebayo; Adejoke O. Dele-Rotimi. On Quasi-Newton Method for Solving Unconstrained Optimization Problems. Am. J. Appl. Math. 2015, 3(2), 47-50. doi: 10.11648/j.ajam.20150302.13

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AMA Style

Felix Makanjuola Aderibigbe, Kayode James Adebayo, Adejoke O. Dele-Rotimi. On Quasi-Newton Method for Solving Unconstrained Optimization Problems. Am J Appl Math. 2015;3(2):47-50. doi: 10.11648/j.ajam.20150302.13

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@article{10.11648/j.ajam.20150302.13,
  author = {Felix Makanjuola Aderibigbe and Kayode James Adebayo and Adejoke O. Dele-Rotimi},
  title = {On Quasi-Newton Method for Solving Unconstrained Optimization Problems},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {47-50},
  doi = {10.11648/j.ajam.20150302.13},
  url = {https://doi.org/10.11648/j.ajam.20150302.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150302.13},
  abstract = {This paper discusses the use of quasi-Newton method algorithm employed in solving unconstrained optimization problems. The method is aimed at circumventing the computational rigours undergone using the Newton’s method.The Quasi –Newton method algorithm was tested on some benced mark problems with the results compared with the Conjugate Gradient Method. The results gotten using the Quasi-Newton Method compared favourably with results of existing CGM algorithm.},
 year = {2015}
}

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TY  - JOUR
T1  - On Quasi-Newton Method for Solving Unconstrained Optimization Problems
AU  - Felix Makanjuola Aderibigbe
AU  - Kayode James Adebayo
AU  - Adejoke O. Dele-Rotimi
Y1  - 2015/02/26
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DO  - 10.11648/j.ajam.20150302.13
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JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
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AB  - This paper discusses the use of quasi-Newton method algorithm employed in solving unconstrained optimization problems. The method is aimed at circumventing the computational rigours undergone using the Newton’s method.The Quasi –Newton method algorithm was tested on some benced mark problems with the results compared with the Conjugate Gradient Method. The results gotten using the Quasi-Newton Method compared favourably with results of existing CGM algorithm.
VL  - 3
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Author Information

Felix Makanjuola Aderibigbe

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Kayode James Adebayo

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Adejoke O. Dele-Rotimi

Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria

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APA Style

Felix Makanjuola Aderibigbe, Kayode James Adebayo, Adejoke O. Dele-Rotimi. (2015). On Quasi-Newton Method for Solving Unconstrained Optimization Problems. American Journal of Applied Mathematics, 3(2), 47-50. https://doi.org/10.11648/j.ajam.20150302.13

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ACS Style

Felix Makanjuola Aderibigbe; Kayode James Adebayo; Adejoke O. Dele-Rotimi. On Quasi-Newton Method for Solving Unconstrained Optimization Problems. Am. J. Appl. Math. 2015, 3(2), 47-50. doi: 10.11648/j.ajam.20150302.13

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AMA Style

Felix Makanjuola Aderibigbe, Kayode James Adebayo, Adejoke O. Dele-Rotimi. On Quasi-Newton Method for Solving Unconstrained Optimization Problems. Am J Appl Math. 2015;3(2):47-50. doi: 10.11648/j.ajam.20150302.13

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@article{10.11648/j.ajam.20150302.13,
  author = {Felix Makanjuola Aderibigbe and Kayode James Adebayo and Adejoke O. Dele-Rotimi},
  title = {On Quasi-Newton Method for Solving Unconstrained Optimization Problems},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {47-50},
  doi = {10.11648/j.ajam.20150302.13},
  url = {https://doi.org/10.11648/j.ajam.20150302.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150302.13},
  abstract = {This paper discusses the use of quasi-Newton method algorithm employed in solving unconstrained optimization problems. The method is aimed at circumventing the computational rigours undergone using the Newton’s method.The Quasi –Newton method algorithm was tested on some benced mark problems with the results compared with the Conjugate Gradient Method. The results gotten using the Quasi-Newton Method compared favourably with results of existing CGM algorithm.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - On Quasi-Newton Method for Solving Unconstrained Optimization Problems
AU  - Felix Makanjuola Aderibigbe
AU  - Kayode James Adebayo
AU  - Adejoke O. Dele-Rotimi
Y1  - 2015/02/26
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150302.13
DO  - 10.11648/j.ajam.20150302.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 47
EP  - 50
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150302.13
AB  - This paper discusses the use of quasi-Newton method algorithm employed in solving unconstrained optimization problems. The method is aimed at circumventing the computational rigours undergone using the Newton’s method.The Quasi –Newton method algorithm was tested on some benced mark problems with the results compared with the Conjugate Gradient Method. The results gotten using the Quasi-Newton Method compared favourably with results of existing CGM algorithm.
VL  - 3
IS  - 2
ER  -

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