A primal-dual exterior point algorithm for linear programming problems

Authors

  • Nikolaos Samaras Department of Applied Informatics, University of Macedonia Greece, Thessaloniki, Greece
  • Angelo Sifelaras Department of Applied Informatics, University of Macedonia Greece, Thessaloniki, Greece
  • Charalampos Triantafyllidis Department of Applied Informatics, University of Macedonia Greece, Thessaloniki, Greece

DOI:

https://doi.org/10.2298/YJOR0901123S

Keywords:

Linear optimization, simplex-type algorithms, primal-dual exterior point algorithm, computational study

Abstract

The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

References

Andersen, E.D., Ye, Y. (1996) Combining interior-point and pivoting algorithms for linear programming. Management Science, 42(12): 1719

Bazarra, M.S., Jarvis, J.J., Sherali, H.D. (2005) Linear programming and network flows. NY: John Wiley & Sons

Bertsimas, D., Tsitsiklis, J.N. (1997) Introduction to linear optimization. Athena Scientific

Bland, R.G. (1977) New finite pivoting rules for the simplex method. Mathematics of Operations Research, 2(2): 103

Dantzig, G.B. (1963) Linear programming and extensions. Princeton, NJ: Princeton University Press

Gondzio, J. (1996) Multiple centrality corrections in a primal-dual method for linear programming. Computational Optimization and Applications, 6, 137-156

Paparrizos, K., Samaras, N., Stephanides, G. (2003) A new efficient primal dual simplex algorithm. Computers & Operations Research, 30(9): 1383

Paparrizos, K. (1997) 'Pivoting algorithms generating two paths. u: ISMP '97, Lausanne: EPFL

Samaras, N. (2001) Computational improvements and efficient implementation of two path pivoting algorithms. Macedonia: Department of Applied Informatics, PhD Thesis

Triantafyllidis, Ch. (2005) Comparative computational study on Exterior Point Algorithms. Macedonia: University - Department of Applied Informatics, BSc Thesis

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Published

2009-03-01

Issue

Vol. 19 No. 1 (2009)

Section

Research Articles

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