On the simplex algorithm initializing This paper discusses the importance of a starting point in the simplex algorithm. Three different methods for finding a basic feasible solution are compared throughout performed numerical test examples. We show that our two methods on the Netlib test problems have better performances than the classical algorithm for finding initial solution. The comparison of the introduced optimization softwares is based on the number of iterative steps and on the required CPU time. It is pointed out that on average it takes more iterations to determine the starting point than the number of iterations required by the simplex algorithm to find the optimal solution.

References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Saito, G.; Corley, H.W.; Rosenberger, Jay M.; Sung, Tai-Kuan; Noroziroshan, Alireza: Constraint optimal selection techniques (COSTs) for nonnegative linear programming problems (2015)
  2. Boonperm, Aua-aree; Sinapiromsaran, Krung: Artificial-free simplex algorithm based on the non-acute constraint relaxation (2014)
  3. Du, Xiuli; Cui, Dong; Hou, Benwei: An initial population improvement strategy of empirical genetic-simplex algorithm (2014)
  4. Stojković, Nebojša V.; Stanimirović, Predrag S.; Petković, Marko D.; Milojković, Danka S.: On the simplex algorithm initializing (2012)
  5. Al-Najjar, Camelia; Malakooti, Behnam: Hybrid-LP: finding advanced starting points for simplex, and pivoting LP methods (2011)
  6. Li, Wei; Li, Haohao: On simplex method with most-obtuse-angle rule and cosine rule (2011)
  7. Malakooti, Behnam; Al-Najjar, Camelia: The complex interior-boundary method for linear and nonlinear programming with linear constraints (2010)
  8. Nabli, Hédi: An overview on the simplex algorithm (2009)
  9. Yeh, Wei-Chang; Corley, H.W.: A simple direct cosine simplex algorithm (2009)
  10. Arsham, H.: A computationally stable solution algorithm for linear programs (2007)
  11. Arsham, Hossein: A hybrid gradient and feasible direction pivotal solution algorithm for general linear programs (2007)
  12. Hu, Jian-Feng: A note on “An improved initial basis for the simplex algorithm” (2007)
  13. Arsham, H.; Cimperman, G.; Damij, N.; Damij, T.; Grad, J.: A computer implementation of the push-and-pull algorithm and its computational comparison with LP simplex method (2005)
  14. Vieira, Hélcio jun.; Pereira Estellita Lins, Marcos: An improved initial basis for the simplex algorithm (2005)
  15. Papamanthou, Charalampos; Paparrizos, Konstantinos; Samaras, Nikolaos: Computational experience with exterior point algorithms for the transportation problem (2004)
  16. Arsham, H.; Damij, T.; Grad, J.: An algorithm for simplex tableau reduction: The push-to-pull solution strategy (2003)
  17. Arsham, Hossein; Gradisar, Miro; Stemberger, Mojca Indihar: Linearly constrained global optimization: a general solution algorithm with applications. (2003)
  18. Arsham, H.: Initialization of the simplex algorithm: An artificial-free approach (1997)