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Title

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 :
Style #
MLA Ahmad Khaldi. "Improving Karmarker Algorithm to Obtain Optimal Solution." Galoitica: Journal of Mathematical Structures and Applications, Vol. 3, No. 2, 2023 ,PP. 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
APA Ahmad Khaldi. (2023). Improving Karmarker Algorithm to Obtain Optimal Solution. Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 ( 2 ), 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
Chicago Ahmad Khaldi. "Improving Karmarker Algorithm to Obtain Optimal Solution." Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 no. 2 (2023): 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
Harvard Ahmad Khaldi. (2023). Improving Karmarker Algorithm to Obtain Optimal Solution. Journal of Galoitica: Journal of Mathematical Structures and Applications, 3 ( 2 ), 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
Vancouver Ahmad Khaldi. Improving Karmarker Algorithm to Obtain Optimal Solution. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2023); 3 ( 2 ): 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)
IEEE Ahmad Khaldi, Improving Karmarker Algorithm to Obtain Optimal Solution, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 3 , No. 2 , (2023) : 28-35 (Doi   :  https://doi.org/10.54216/GJMSA.030204)