Galoitica: Journal of Mathematical Structures and Applications

Journal DOI

https://doi.org/10.54216/GJSMA

Submit Your Paper

2834-5568ISSN (Online)
Full Length Article

Galoitica: Journal of Mathematical Structures and Applications

Volume 3 , Issue 2 , PP: 28-35, 2023 | Cite this article as | XML | Html | PDF

Improving Karmarker Algorithm to Obtain Optimal Solution

Ahmad Khaldi 1 *

  • 1 Mutah University, Faculty of Science, Jordan - (khaldiahmad1221@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.030204

    Received: October 12, 2022 Accepted: January 02, 2023
    Abstract

    In this research, the Karmarker's method of linear programming was improved using the eigenvector of the starting point with all iterations.Where the improvement showed that Karmarker's method can be reduced in a theoretical way by direct method without iterations and access to the optimal solution. The procedure was also Comparison of the two methods and the results of the proposed method were faster and better to reach.

    Keywords :

    Karmarker's algorithm , optimal solution , linear programming.

    References

    [1]  Edwin, K. P. and Stanislaw, H. Z., "An Introduction To Optimization", by John Wily & Sons, Inc., America, 2001.

    [2]  Karloff, H., "Linear Programming", Birkhauser .Boston.Berlin, 2009.

    [3]  Karmarker, N., "A new polynomial time algorithm for linear programming", Combinatorica 4 (1984), 373 -395.

    [4]  Kebbiche, Z., Keraghel, A. and Yassine, A., " An infeasible interior point method for the monotone linear

    [5]  complementarity problem ", Int. Journal of Math. Analysis, Vol. 1, 2007, No. 17, 841 – 849.

    [6]  Nash, S. G. and Sofer, A.," Linear and Nonlinear Programming", New York: McGraw-Hill, 1996.

    [7]  Nemirovski, A. S. and Todd, M. J., " Interior-point methods for optimization ", Acta Numerica (2008), pp.191–234

    [8]  Peng, j., Roos, C. and Terlaky, T.," A new and efficient large-update interior-point method for linear optimization", Tom 6, 2001,Ν2 4.

    [9]  Winston, W., L.,"Operation Research Application and Algorithm", Indian, 1994.

    [10]  Zsuzsanna, S´ and M´arta, K., " On interior-point methods and simplex method in linear programming", An. S¸t. Univ. Ovidius Constant a Vol. 11,2003 , No. 2, 155–162.

    Cite This Article As :
    Ahmad Khaldi. "Improving Karmarker Algorithm to Obtain Optimal Solution." Full Length Article, Vol. 3, No. 2, 2023 ,PP. 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
    Ahmad Khaldi. (2023). Improving Karmarker Algorithm to Obtain Optimal Solution. Journal of , 3 ( 2 ), 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
    Ahmad Khaldi. "Improving Karmarker Algorithm to Obtain Optimal Solution." Journal of , 3 no. 2 (2023): 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
    Ahmad Khaldi. (2023). Improving Karmarker Algorithm to Obtain Optimal Solution. Journal of , 3 ( 2 ), 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
    Ahmad Khaldi. Improving Karmarker Algorithm to Obtain Optimal Solution. Journal of , (2023); 3 ( 2 ): 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
    Ahmad Khaldi, Improving Karmarker Algorithm to Obtain Optimal Solution, Journal of , Vol. 3 , No. 2 , (2023) : 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)