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 |
Iterative Point, Non Polynomial, Unconstrained Optimization, Conjugate Gradient Method, Descent Direction, Exact Line Search, Iterative Scheme
| [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. |
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
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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Download@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}
}
TY - JOUR T1 - Minimization of Unconstrained Nonpolynomial Large-Scale Optimization Problems Using Conjugate Gradient Method Via Exact Line Search AU - Adam Ajimoti AU - Onah David Ogwumu Y1 - 2017/04/07 PY - 2017 N1 - https://doi.org/10.11648/j.ajmme.20170101.13 DO - 10.11648/j.ajmme.20170101.13 T2 - American Journal of Mechanical and Materials Engineering JF - American Journal of Mechanical and Materials Engineering JO - American Journal of Mechanical and Materials Engineering SP - 10 EP - 14 PB - Science Publishing Group SN - 2639-9652 UR - https://doi.org/10.11648/j.ajmme.20170101.13 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. VL - 1 IS - 1 ER -
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