:: International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies
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ISSN 2228-9860
eISSN 1906-9642
CODEN: ITJEA8
FEATURE PEER-REVIEWED ARTICLE
Vol.12(1) (2021) |
An Approximate Analytical Solution of Non-Linear Fractional-Order Constrained Optimization Problem Using Optimal Homotopy Analysis Method
Oluwaseun Olumide Okundalaye, Wan Ainun Mior Othman(Institute of Mathematical Sciences, Faculty of Science, University of Malaya, MALAYSIA ).
Disciplinary: Mathematics.
Keywords: Penalty Function; Fractional Differential Equations; Constrained Optimization Problem; Convergence-Control Parameters; Homotopy Analysis Method.
AbstractWe present an optimal homotopy analysis method (OHAM) to find an accurate approximate analytic solution (AAS) for non-linear fractional-order constrained optimization problem (FOCOP). The previous analytical approximate method (AAM) of solving FOCOP possesses no norms for the convergence of the infinite series solution. OHAM provides an independent way of choosing proper values of the control-convergence parameter (CCP), auxiliary linear operator, and enables us to control and govern the convergence area of the series solution produced by a squared residual error optimization technique. Numerical comparisons of OHAM with Runge-Kutta fourth-order (RK4) method for accuracy. Some examples from the CUTEr library were used to indicate the correctness and relevance of the suggested techniques.Paper ID: 12A1D
Cite this article:
Saad, A. M., Mohamad, M. B., and Tsong, C. K. (2021). An Approximate Analytical Solution of Non-Linear Fractional-Order Constrained Optimization Problem Using Optimal Homotopy Analysis Method. International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies, 12(1), 12A1D, 1-13. http://doi.org/10.14456/ITJEMAST.2021.4
References
- Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational & Applied Mathematics, 279, 57-66.
- Evirgen, F., Ozdemir, N. (2011). Multistage domian decomposition method for solving NLP problems over a non-linear fractional dynamical system. Journal of Computational & Nonlinear Dynamics, 6(2).
- Evirgen, F., Ozdemir, N. (2012). A fractional-order dynamical trajectory approach for optimization problem with HPM. Fractional Dynamics & Control, 145-155.
- Evirgen, F. (2016). Analyze the optimal solutions of optimization problems by means of fractional gradient based system using vim. International Journal of Optimization & Control: Theories & Applications, 6(2), 75-83.
- Evirgen, F. (2017). Conformable fractional gradient based dynamic system for constrained optimization problem. Acta Physica Polonica A, 132(3), 1066-1069.
- Franceschi, L., Donini, M., Frasconi, P., Pontil M. (2017). Forward and reverse gradient-based hyperparameter optimization. Proc. the 34th International Conference on Machine Learning, 70, 1165-1173.
- Liao, S. (2010) An optimal homotopy-analysis approach for strongly non-linear differential equations. Communications in Nonlinear Science & Numerical Simulation, 15(8), 2003-2016.
- Nguyen BT, Bai Y, Yan X, Yang T. (2019). Perturbed smoothing approach to the lower order exact penalty functions for non-linear inequality constrained optimization. Tamkang Journal of Mathematics, 50(1), 37-60.
- Niu, Z., Wang, C. A. (2010). One-step optimal homotopy analysis method for non-linear differential equations. Communications in Nonlinear Science and Numerical Simulation, 15(8), 2026-2036.
- Odibat, Z. (2019). On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to non-linear fractional differential equations. Applied Numerical Mathematics, 137, 203-212.
- Odibat, Z. (2020). An improved optimal homotopy analysis algorithm for non-linear differential equations. Journal of Mathematical Analysis and Applications, 124089.
- Pu, Y.F., Zhou, J. L., Zhang, Y., Zhang, N., Huang, G., Siarry, P. (2013). Fractional extreme value adaptive training method: fractional steepest descent approach. IEEE Transactions on Neural Networks & Learning Systems, 26(4), 653-662.
- Schittkowski, K. (2012). More Test Examples for Nonlinear Programming Codes. Springer-Verlag, Springer Science & Business Media, 282.
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