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An Efficient Fifth-Order Method for Linear Optimization

Author

Listed:
  • Youssef EL Foutayeni

    (Hassan II University, Faculté des Sciences Ben M’Sik, Av Driss El Harti
    Unit for Mathematical and Computer Modeling of Complex Systems, IRD)

  • Hicham EL Bouanani

    (Hassan II University)

  • Mohamed Khaladi

    (Cadi Ayyad University
    UMMISCO UMI 209 IRD/UPMC)

Abstract

In this paper, we present an efficient fifth-order method for solving the standard linear optimization problems. In order to do this, we show that solving this problem is equivalent to solving a system of nonlinear equations. Therefore, we build a sequence of functions giving an approximate solution of this system. To find this approximation, we give an algorithm, which is based on the idea of the Sharma’s method. Computational efficiency, in its general form, is discussed, and a comparison between the efficiency of proposed technique and existing one is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the examples.

Suggested Citation

  • Youssef EL Foutayeni & Hicham EL Bouanani & Mohamed Khaladi, 2016. "An Efficient Fifth-Order Method for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 189-204, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-016-0896-z
    DOI: 10.1007/s10957-016-0896-z
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