A New Hybrid Conjugate Gradient Method with Guaranteed Descent for Unconstraint Optimization
DOI:
https://doi.org/10.23851/mjs.v28i3.114Abstract
The conjugate gradient method an efficient technique for solving the unconstrained optimization problem. In this paper, we propose a new hybrid nonlinear conjugate gradient methods, which have the descent at every iteration and globally convergence properties under certain conditions. The numerical results show that new hybrid method are efficient for the given test problems.
References
Andrie N. (2008) ' An Unconstrained Optimization Test functions collection ' Advanced Modeling and optimization. 10, pp.147-161.
AndreiN., (2009),' New hybrid conjugate gradient algorithms for unconstrained optimization, Encyclopedia of Optimization, pp.2560-2571. DOI: https://doi.org/10.1007/978-0-387-74759-0_441
Andrei N., (2008),' A hybrid conjugate gradient algorithm for unconstrained optimization as a convex combination of Hestenes-Stiefel and Dai-Yuan, Studies in Informatics and Control, 17, 1, pp. 55–70.
Basim A. H. and Haneen A. A., (2016), New Nonlinear Conjugate Gradient Formulas for Solving Unconstrained Optimization Problems, Al-Mustansiriyah Journal of Science, 3, pp. 82-88.
Dai Y. H. and Yuan Y., (1999). A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. optimization, pp. 177-182. DOI: https://doi.org/10.1137/S1052623497318992
Fletcher R. and Reeves C. M.,(1964). Funtion minimization by conjagate gradients, Computer Journal 7, pp. 149-154. DOI: https://doi.org/10.1093/comjnl/7.2.149
Fletcher R., (1989). Practical Method of Optimization (2nd Edition), John Wiley and Sons, New York .
Hestenes M. R. and Stiefel E., (1952). Methods of conjugate gradients for solving linear systems, Journal of Research of National Burean of Standard,49, pp. 409-436. DOI: https://doi.org/10.6028/jres.049.044
Hager W.W.and Zhang H., (2006),' A survey of nonlinear conjugate gradient methods, Pacific journal of Optimization, 2, pp. 35–58.
Ladislav L. and Jan V. , (2015) ,'Nonlinear conjugate gradient methods, Programs and Algorithms of Numerical Mathematics, Proceedings of Seminar. Institute of Mathematics AS CR, pp.130--135.
Liu Y. and Storey C. , (1991) ' Eff-icient generalized conjugate gradients algorithms ' Part 1 : Theory. J. Optimization Theory and Applications, 69, pp. 129-137. DOI: https://doi.org/10.1007/BF00940464
Polak E. and Ribiere G., (1969) . Note sur la Convergence de Directions Conjugate, Revue Francaise Informant, Reserche. Opertionelle16, pp. 35-43. DOI: https://doi.org/10.1051/m2an/196903R100351
Downloads
Published
How to Cite
Issue
Section
License
The journal has no restrictions for the author to hold the copyrights of his articles. The journal does not allow authors to republish the same article in other journals or conferences that is published in one of its volumes.
