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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2016 / Cilt: 6 - Sayı: 2

Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM

Fırat EVİRGEN
Pages
75–83
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The comparisons amongthe multistage variational iteration method, the variational iteration method and the fourth orderRunge-Kutta method in fractional and integer order show that fractional order model and techniquescan be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programmingproblems.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a class of Nonlinear Programming problem is modeled with gradient basedsystem of fractional order differential equations in Caputo's sense.
📊
Key Findings & Data:To see the overlap between theequilibrium point of the fractional order dynamic system and the optimal solution of the NLP problemin a longer timespan the Multistage Variational teration Method is applied.
💡
Conclusion & Impact:The comparisons amongthe multistage variational iteration method, the variational iteration method and the fourth orderRunge-Kutta method in fractional and integer order show that fractional order model and techniquescan be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programmingproblems.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, a class of Nonlinear Programming problem is modeled with gradient basedsystem of fractional order differential equations in Caputo's sense. To see the overlap between theequilibrium point of the fractional order dynamic system and the optimal solution of the NLP problemin a longer timespan the Multistage Variational teration Method is applied. The comparisons amongthe multistage variational iteration method, the variational iteration method and the fourth orderRunge-Kutta method in fractional and integer order show that fractional order model and techniquescan be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programmingproblems.

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Cite This Article

EVİRGEN, F. (2022). Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 6 - Sayı: 2, 75–83. https://ajindex.com/articles/440697

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References (18)

  1. Luenberger, D.G. and Ye, Y., Linear and Nonlinear Programming, Third Edition, Springer, New York (2008)
  2. Sun, W. and Yuan, Y.X., Optimization Theory and Methods: Nonlinear Programming, Springer-Verlag, New York (2006)
  3. Arrow, K.J., Hurwicz, L. and Uzawa, H., Studies in Linear and Non-Linear Programming, Stanford University Press, California (1958)
  4. Fiacco, A.V. and Mccormick, G.P., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, New York (1968)
  5. Yamashita, H., Differential equation approach to nonlinear programming. Math. Program., 18, 155-168 (1976)
  6. Botsaris, C.A., Differential gradient methods. J. Math. Anal. Appl., 63, 177-198 (1978)
  7. Brown, A.A. and Bartholomew-Biggs, M.C., ODE versus SQP methods for constrained optimization. J. Optim. Theory Appl., 62, 371-389 (1989)
  8. Evtushenko, Y.G. and Zhadan, V.G., Stable barrier-projection and barrier-Newton methods in nonlinear programming. Opt. Software, 3, 237-256 (1994)
  9. Schropp, J., A dynamical system approach to constrained minimization. Numer. Funct. Anal. Optim., 21, 537-551 (2000)
  10. Wang, S., Yang, X.Q. and Teo, K.L., A uni- fied gradient flow approach to constrained nonlinear optimization problems. Comput. Optim. Appl., 25, 251-268 (2003)
  11. Jin, L., Zhang, L.-W. and Xiao, X., Two differential equation systems for equalityconstrained optimization. Appl. Math. Comput., 190, 1030-1039 (2007)
  12. Jin, L., A stable differential equation approach for inequality constrained optimization problems. Appl. Math. Comput., 206, 186-192 (2008)
  13. Shikhman, V. and Stein, O., Constrained optimization: projected gradient flows. J. Optim. Theory Appl., 140, 117-130 (2009)
  14. Ozdemir, N. and Evirgen, F., A dynamic ¨ system approach to quadratic programming problems with penalty method. Bull. Malays. Math. Sci. Soc., 33, 79-91 (2010)
  15. Podlubny, I., Fractional Differential Equations, Academic Press, New York (1999)
  16. Bulut, H., Baskonu¸s, H.M., Belgacem, F.B.M., The analytical solution of some fractional ordinary differential equations by the Sumudu transform method. Abstr. Appl. Anal., Art. ID 203875, 6 pp. (2013)
  17. Baskonu¸s, H.M., Mekkaou, T., Hammouch, Z. and Bulut, H., Active control of a chaotic fractional order economic system. Entropy, 17(8), 5771-5783 (2015)
  18. Baskonu¸s, H.M., Bulut, H., On the numerical solutions of some fractional ordinary differential equations by fractional AdamsBashforth-Moulton method. O