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2017 | 132 | 3 | 1066-1069
Article title

Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem

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EN
Abstracts
EN
A conformable fractional gradient based dynamic system with a steepest descent direction is proposed in this paper for a class of nonlinear programming problems. The solutions of the dynamic system, modelled with the conformable fractional derivative are investigated to obtain the minimizing point of the optimization problem. For this purpose, we use a step variational iteration method, adapted to use a conformable integral definition. Numerical simulations and comparisons show that the conformable fractional gradient based dynamic system is both feasible and efficient for a certain class of equality constrained optimization problems. Furthermore, the step variational iteration method, combined with the conformable integral definition, is a reliable tool for solving a system of fractional differential equations.
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EN
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Year
Volume
132
Issue
3
Pages
1066-1069
Physical description
Dates
published
2017-09
Contributors
author
  • Balıkesir University, Department of Mathematics, Balıkesir, Turkey
References
  • [1] A.T. Özturan, Acta Phys. Pol. A 128, B-93 (2015), doi: 10.12693/APhysPolA.128.B-93
  • [2] A. Recioui, Acta Phys. Pol. A 128, B-7 (2015), doi: 10.12693/APhysPolA.128.B-7
  • [3] M.J. Pazdanowski, Acta Phys. Pol. A 128, B-213 (2015), doi: 10.12693/APhysPolA.128.B-213
  • [4] A.T. Özturan, Acta Phys. Pol. A 130, 14 (2016), doi: 10.12693/APhysPolA.130.14
  • [5] D.G. Luenberger, Y. Ye, Linear and Nonlinear Programming, 3rd ed., Springer, New York 2008
  • [6] K.J. Arrow, L. Hurwicz, H. Uzawa, Studies in Linear and Non-Linear Programming, Stanford University Press, California 1958
  • [7] A.V. Fiacco, G.P. Mccormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, New York 1968
  • [8] H. Yamashita, Math. Program. 18, 155 (1976)
  • [9] C.A. Botsaris, J. Math. Anal. Appl. 63, 177 (1978), doi: 10.1016/0022-247X(78)90114-2
  • [10] A.A. Brown, M.C. Bartholomew-Biggs, J. Optim. Theory Appl. 62, 371 (1989), doi: 10.1007/BF00939812
  • [11] Y.G. Evtushenko, V.G. Zhadan, Opt. Meth. Software 3, 237 (1994), doi: 10.1080/10556789408805567
  • [12] J. Schropp, I. Singer Numer. Funct. Anal. Optim. 21, 537 (2000), doi: 10.1080/01630560008816971
  • [13] S. Wang, X.Q. Yang, K.L. Teo, Comput. Optim. Appl. 25, 251 (2003), doi: 10.1023/A:1022973608903
  • [14] L. Jin, L.-W. Zhang, X. Xiao, Appl. Math. Comput. 190, 1030 (2007)
  • [15] L. Jin, Appl. Math. Comput. 206, 186 (2008)
  • [16] V. Shikhman, O. Stein, J. Optim. Theory Appl. 140, 117 (2009), doi: 10.1007/s10957-008-9445-8
  • [17] N. Özdemir, F. Evirgen, Bull. Malays. Math. Sci. Soc. 33, 79 (2010)
  • [18] I. Podlubny, Fractional Differential Equations, Academic Press, New York 1999
  • [19] J.H. He, Commun. Nonlinear Sci. Numer. Simul. 2, 235 (1997), doi: 10.1016/S1007-5704(97)90008-3
  • [20] R.Y. Molliq, N.S.M. Noorani, R.R. Ahmad, A.K. Alomari, Sains Malaysiana 42, 347 (2013)
  • [21] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, J. Comput. Appl. Math. 264, 65 (2014), doi: 10.1016/j.cam.2014.01.002
  • [22] T. Abdeljawad, J. Comput. Appl. Math. 279, 57 (2015), doi: 10.1016/j.cam.2014.10.016
  • [23] F. Evirgen, N. Özdemir, J. Comput. Nonlinear Dyn. 6, 021003 (2011), doi: 10.1115/1.4002393
  • [24] F. Evirgen, N. Özdemir, A fractional order dynamical trajectory approach for optimization problem with HPM. Fractional Dynamics and Control, Eds. D. Baleanu, J.A.T. Machado, A.C.J. Luo, Springer 2012, p. 145
  • [25] F. Evirgen, Int. J. Optimization Control: Theor. Applicat. (IJOCTA) 6, 75 (2016)
  • [26] W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes, Springer-Verlag, Berlin 1981
  • [27] K. Schittkowski, More Test Examples For Nonlinear Programming Codes, Springer, Berlin 1987
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-app132z3-iip068kz
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