Exterior Point Simplex Algorithm

Part of the Springer Optimization and Its Applications book series (SOIA, volume 127)


The exterior point simplex algorithm is a simplex-type algorithm that moves in the exterior of the feasible solution and constructs basic infeasible solutions instead of constructing feasible solutions like simplex algorithm does. This chapter presents the exterior point simplex algorithm. Numerical examples are presented in order for the reader to understand better the algorithm. Furthermore, an implementation of the algorithm in MATLAB is presented. The implementation is modular allowing the user to select which scaling technique and basis update method will use in order to solve LPs. Finally, a computational study over benchmark LPs and randomly generated sparse LPs is performed in order to compare the efficiency of the proposed implementation with the revised primal simplex algorithm presented in Chapter  8.

Supplementary material (7 kb)
chapter 10 (Zip 7 kb)


  1. 1.
    Bixby, R. E. (1992). Implementing the simplex method: The initial basis. ORSA Journal on Computing, 4, 267–284.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Carstens, D. M. (1968) Crashing techniques. In W. Orchard-Hays (Ed.), Advanced linear-programming computing techniques (pp. 131–139). New York: McGraw-Hill.Google Scholar
  3. 3.
    Gould, N. I. M., & Reid, J. K. (1989). New crash procedures for large systems of linear constraints. Mathematical Programming, 45, 475–501.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Maros, I., & Mitra, G. (1998). Strategies for creating advanced bases for large-scale linear programming problems. INFORMS Journal on Computing, 10, 248–260.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Paparrizos, K. (1991). An infeasible exterior point simplex algorithm for assignment problems. Mathematical Programming, 51(1–3), 45–54.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Paparrizos, K. (1993). An exterior point simplex algorithm for (general) linear programming problems. Annals of Operations Research, 47, 497–508.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Paparrizos, K., Samaras, N., & Sifaleras, A. (2015). Exterior point simplex-type algorithms for linear and network optimization problems. Annals of Operations Research, 229(1), 607–633.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Paparrizos, K., Samaras, N., & Stephanides, G. (2003). An efficient simplex type algorithm for sparse and dense linear programs. European Journal of Operational Research, 148(2), 323–334.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Paparrizos, K., Samaras, N., & Stephanides, G. (2003). A new efficient primal dual simplex algorithm. Computers & Operations Research, 30(9), 1383–1399.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Paparrizos, K., Samaras, N., & Tsiplidis, K. (2009). Pivoting algorithms for (LP) generating two paths. Encyclopedia of optimization, 2nd edition, 2965–2969.Google Scholar
  11. 11.
    Ploskas, N., & Samaras, N. (2015). Efficient GPU-based implementations of simplex type algorithms. Applied Mathematics and Computation, 250, 552–570.CrossRefGoogle Scholar
  12. 12.
    Samaras, N. (2001). Computational improvements and efficient implementation of two path pivoting algorithms. Ph.D. dissertation, Department of Applied Informatics, University of Macedonia.Google Scholar
  13. 13.
    Triantafyllidis, C., & Samaras, N. (2014). Three nearly scaling-invariant versions of an exterior point algorithm for linear programming. Optimization, 64(10), 2163–2181.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Applied InformaticsUniversity of MacedoniaThessalonikiGreece

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