THE NEW RANK ONE CLASS FOR UNCONSTRAINED PROBLEMS SOLVING
DOI:
https://doi.org/10.25271/sjuoz.2023.11.2.1049Keywords:
Quasi-Newton, Symmetric Rank One, Positive Definite Matrix, Unconstrained Optimization, Nonlinear OptimizationAbstract
One of the most well-known methods for unconstrained problems is the quasi-Newton approach, iterative solutions. The great precision and quick convergence of the quasi-Newton methods are well recognized. In this work, the new algorithm for the symmetric rank one SR1 method is driven.
The strong Wolfe line search criteria define the step length selection. We also proved the new quasi-Newton equation and positive definite matrix theorem. Preliminary computer testing on the set of fourteen unrestricted optimization test functions leads to the conclusion that this new method is more effective and durable than the implementation of classical SR1 method in terms of iterations count and functions.
References
Basheer M. S., Khalil K. A., Zeyad M. A. (2016). Partial Davidon, Fletcher and Powell (DFP) of quasi newton method for unconstrained optimization. Tikrit Journal of Pure Science, 21(6),180-186.
Cullum, j., and Brayton, R. K. (1979) Some Remarks on the Symmetric Rank-One Update, Journal of Optimization Theory and Applications. 27(4), 493-519.
Dennis, J.E., Schnabel, R.B. (1982). Numerical Methods for Nonlinear Equations and Unconstrained Optimization Prentice Hall, Englewood Cliffs.
Farzin M., Malik A. H. and Wah J. L. (2009). Memoryless Modified Symmetric Rank-One Method for Large-Scale Unconstrained Optimization, American Journal of Applied Sciences,6(12),2054-2059.
Fletcher, R. (1980). Practical Methods of Optimization. Wiley, New York.
Gill, P.E., Murray, W., Wright, M.H. (1981). Practical Optimization. Academic, London.
Issam A. R. M., Basim A. H., Aadil A. (2022). New Self-scaling Quasi-Newton methods for unconstrained optimization. International Journal of Mathematics and Computer Science,17(3), 1061-1077.
Mahmood S. S. and Farqad H. (2017). On Extended Symmetric Rank One Update for Unconstrained Optimization,” J. of Education. Special issued, 206-220.
Philipp H. Martin K.(2013). Quasi-Newton Methods: A New Direction. Journal of Machine Learning Research, 14, 843-865..
Saad Sh. M. and Jaafer H. E. (2022). New Class of Rank 1 Update for Solving Unconstrained Optimization Problem. Iraqi Journal of Science, 63(2), 683-689.
Wah J. L., Malik A. H.(2009).A restarting approach for the symmetric rank one update for unconstrained optimization. Comput. Optim. Appl.,42, 327–334.
Zhang J. and Xu Ch.(2001). Properties and Numerical Performance of Modified quasi–Newton Methods Equations. Elsevier, J. of Comp. and App. Math,137, 269-278.
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