PL EN


Preferences help
enabled [disable] Abstract
Number of results
2017 | 132 | 3 | 1062-1065
Article title

Solution of a Class of Optimization Problems Based on Hyperbolic Penalty Dynamic Framework

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
In this study, a gradient-based dynamic system is constructed in order to solve a certain class of optimization problems. For this purpose, the hyperbolic penalty function is used. Firstly, the constrained optimization problem is replaced with an equivalent unconstrained optimization problem via the hyperbolic penalty function. Thereafter, the nonlinear dynamic model is defined by using the derivative of the unconstrained optimization problem with respect to decision variables. To solve the resulting differential system, a steepest descent search technique is used. Finally, some numerical examples are presented for illustrating the performance of the nonlinear hyperbolic penalty dynamic system.
Keywords
EN
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] L. Jin, Appl. Math. Comput. 206, 186 (2008)
  • [14] N. Özdemir, F. Evirgen, Bull. Malays. Math. Sci. Soc. 33, 79 (2010)
  • [15] F. Evirgen, N. Özdemir, J. Comput. Nonlinear Dyn. 6, 021003 (2011), doi: 10.1115/1.4002393
  • [16] F. Evirgen, N. Özdemir, A Fractional Order Dynamical Trajectory Approach for Optimization Problem with HPM, Eds. D. Baleanu, J.A.T. Machado, A.C.J. Luo, Springer, 2012, p. 145
  • [17] F. Evirgen, Int. J. Optim. Control: Th. Applicat. (IJOCTA) 6, 75 (2016)
  • [18] A.E. Xavier, M.Sc. Thesis, Federal University of Rio de Janerio/COPPE, Rio de Janerio 1982
  • [19] A.E. Xavier, Intl. Trans. in Op. Res. 8, 659 (2001), doi: 10.1111/1475-3995.t01-1-00330
  • [20] W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes, Springer-Verlag, Berlin 1981
  • [21] 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-iip067kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.