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Minimization of Unconstrained Nonpolynomial Large-Scale Optimization Problems Using Conjugate Gradient Method Via Exact Line Search

Received: 28 February 2017     Accepted: 22 March 2017     Published: 7 April 2017
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Abstract

The nonlinear conjugate gradient method is an effective iterative method for solving large-scale optimization problems using the iterative scheme x(k+1) = x(k) + αkd(k) where: x(k+1) is the new iterative point, x(k) is the current iterative point, αk is the step-size and d(k) is the descent direction. In this research work, we employed the technique of exact line search to compute the step-size in the iterative scheme mentioned above. The line search technique gave good results when applied to some non-polynomial unconstrained optimization problems.

Published in American Journal of Mechanical and Materials Engineering (Volume 1, Issue 1)
DOI 10.11648/j.ajmme.20170101.13
Page(s) 10-14
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), 2017. Published by Science Publishing Group

Keywords

Iterative Point, Non Polynomial, Unconstrained Optimization, Conjugate Gradient Method, Descent Direction, Exact Line Search, Iterative Scheme

References
[1] Andrei, N. (2008). Unconstrained optimization text functions. Unpub-lished manuscript. Research Institute of Informatics. Bucharest, Romania.
[2] Ali, M. Lecture on Nonlinear unconstrained optimization. School of Computation and Applied Mathematics, University of Witwatersand, Johannesburg, South Africa.
[3] Bamigbola, O. M, Ali, M. and Nwaeze E. (2010). An efficient and convergent conjugate gradient method for unconstrained nonlinear optimization (submitted).
[4] Fletcher, R. and Reeves, C. M. (1964). Function minimization by con-jugate gradient. Computer Journal. Vol. 7, No. 2, pp. 149-154.
[5] Dai, Y. and Yuan, Y. (2000). A nonlinear conjugate gradient with a strong global convergence properties: SIAM Journal on Optimization. Vol. 10, pp. 177-182.
[6] Fletcher, R. (1997). Practical method of optimization, second edition John Wiley, New York.
[7] Polak, E. and Ribiere, G. (1969). Note sur la convergence de directions conjugees. Rev. Francaise Informant Recherche operationlle, 3e Annee 16, pp. 35-43.
[8] Polyak, B. T. (1969). The conjugate gradient in extreme problems. USSR comp. Math. Math. phys. 94-112.
[9] Hestenes, M. R. and Steifel, E. (1952). Method of conjugate gradient for solving linear equations. J. Res. Nat. Bur. Stand, pp. 49.
[10] Liu, Y and Storey, C. (1992). Efficient generalized conjugate gradient algorithms. Journal of Optimization Theory and Applications. Vol. 69, pp. 129-137.
[11] Rao, S. S. (1980). Optimization theory and applications, second edi-tion, Wiley Eastern Ltd., New Delhi.
[12] Getr, G. and Trond, S. (2000). On large-scale unconstrained optimization problems and higher order methods. University of Bergen, Department of Informatics, High Technology Centre N-5020 Bergen, Norway.
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  • APA Style

    Adam Ajimoti, Onah David Ogwumu. (2017). Minimization of Unconstrained Nonpolynomial Large-Scale Optimization Problems Using Conjugate Gradient Method Via Exact Line Search. American Journal of Mechanical and Materials Engineering, 1(1), 10-14. https://doi.org/10.11648/j.ajmme.20170101.13

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    ACS Style

    Adam Ajimoti; Onah David Ogwumu. Minimization of Unconstrained Nonpolynomial Large-Scale Optimization Problems Using Conjugate Gradient Method Via Exact Line Search. Am. J. Mech. Mater. Eng. 2017, 1(1), 10-14. doi: 10.11648/j.ajmme.20170101.13

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    AMA Style

    Adam Ajimoti, Onah David Ogwumu. Minimization of Unconstrained Nonpolynomial Large-Scale Optimization Problems Using Conjugate Gradient Method Via Exact Line Search. Am J Mech Mater Eng. 2017;1(1):10-14. doi: 10.11648/j.ajmme.20170101.13

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  • @article{10.11648/j.ajmme.20170101.13,
      author = {Adam Ajimoti and Onah David Ogwumu},
      title = {Minimization of Unconstrained Nonpolynomial Large-Scale Optimization Problems Using Conjugate Gradient Method Via Exact Line Search},
      journal = {American Journal of Mechanical and Materials Engineering},
      volume = {1},
      number = {1},
      pages = {10-14},
      doi = {10.11648/j.ajmme.20170101.13},
      url = {https://doi.org/10.11648/j.ajmme.20170101.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmme.20170101.13},
      abstract = {The nonlinear conjugate gradient method is an effective iterative method for solving large-scale optimization problems using the iterative scheme x(k+1) = x(k) + αkd(k) where: x(k+1) is the new iterative point, x(k) is the current iterative point, αk is the step-size and d(k) is the descent direction. In this research work, we employed the technique of exact line search to compute the step-size in the iterative scheme mentioned above. The line search technique gave good results when applied to some non-polynomial unconstrained optimization problems.},
     year = {2017}
    }
    

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    T2  - American Journal of Mechanical and Materials Engineering
    JF  - American Journal of Mechanical and Materials Engineering
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    AB  - The nonlinear conjugate gradient method is an effective iterative method for solving large-scale optimization problems using the iterative scheme x(k+1) = x(k) + αkd(k) where: x(k+1) is the new iterative point, x(k) is the current iterative point, αk is the step-size and d(k) is the descent direction. In this research work, we employed the technique of exact line search to compute the step-size in the iterative scheme mentioned above. The line search technique gave good results when applied to some non-polynomial unconstrained optimization problems.
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Author Information
  • Department of Mathematics, University of Ilorin, Ilorin, Nigeria

  • Department of Mathematics, Federal University Wukari, Wukari, Nigeria

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