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Implementation of Interior Point Methods for Large Scale Linear Programming

Author

Listed:
  • Andersen, E.D.
  • Gondzio, J.
  • Meszaros, C.
  • Xu, X.

Abstract

In this paper we give an overview of the mostimportant characteristics of advanced implementations of interior point methods.

Suggested Citation

  • Andersen, E.D. & Gondzio, J. & Meszaros, C. & Xu, X., 1996. "Implementation of Interior Point Methods for Large Scale Linear Programming," Papers 96.3, Ecole des Hautes Etudes Commerciales, Universite de Geneve-.
    • Handle: RePEc:fth:ehecge:96.3
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    Citations

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    Cited by:

    1. Kuo-Ling Huang & Sanjay Mehrotra, 2013. "An empirical evaluation of walk-and-round heuristics for mixed integer linear programs," Computational Optimization and Applications, Springer, vol. 55(3), pages 545-570, July.
    2. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    3. Illes, Tibor & Terlaky, Tamas, 2002. "Pivot versus interior point methods: Pros and cons," European Journal of Operational Research, Elsevier, vol. 140(2), pages 170-190, July.
    4. Maros, Istvan & Haroon Khaliq, Mohammad, 2002. "Advances in design and implementation of optimization software," European Journal of Operational Research, Elsevier, vol. 140(2), pages 322-337, July.
    5. Peng, Jiming & Roos, Cornelis & Terlaky, Tamas, 2002. "A new class of polynomial primal-dual methods for linear and semidefinite optimization," European Journal of Operational Research, Elsevier, vol. 143(2), pages 234-256, December.
    6. J. Peng & C. Roos & T. Terlaky, 2001. "New Complexity Analysis of the Primal–Dual Method for Semidefinite Optimization Based on the Nesterov–Todd Direction," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 327-343, May.
    7. Freund, Robert Michael. & Mizuno, Shinji., 1996. "Interior point methods : current status and future directions," Working papers 3924-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Fernanda Raupp & B. Svaiter, 2009. "Analytic center of spherical shells and its application to analytic center machine," Computational Optimization and Applications, Springer, vol. 43(3), pages 329-352, July.
    9. Terlaky, Tamas, 2001. "An easy way to teach interior-point methods," European Journal of Operational Research, Elsevier, vol. 130(1), pages 1-19, April.
    10. Stojkovic, Nebojsa V. & Stanimirovic, Predrag S., 2001. "Two direct methods in linear programming," European Journal of Operational Research, Elsevier, vol. 131(2), pages 417-439, June.
    11. Jacek Gondzio & Andreas Grothey, 2009. "Exploiting structure in parallel implementation of interior point methods for optimization," Computational Management Science, Springer, vol. 6(2), pages 135-160, May.
    12. Rehfeldt, Daniel & Hobbie, Hannes & Schönheit, David & Koch, Thorsten & Möst, Dominik & Gleixner, Ambros, 2022. "A massively parallel interior-point solver for LPs with generalized arrowhead structure, and applications to energy system models," European Journal of Operational Research, Elsevier, vol. 296(1), pages 60-71.
    13. Maziar Salahi & Renata Sotirov & Tamás Terlaky, 2004. "On self-regular IPMs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 209-275, December.
    14. Salahi, M. & Peyghami, M.R. & Terlaky, T., 2008. "New complexity analysis of IIPMs for linear optimization based on a specific self-regular function," European Journal of Operational Research, Elsevier, vol. 186(2), pages 466-485, April.
    15. Glineur, Francois, 2002. "Improving complexity of structured convex optimization problems using self-concordant barriers," European Journal of Operational Research, Elsevier, vol. 143(2), pages 291-310, December.
    16. Luca Bergamaschi & Jacek Gondzio & Manolo Venturin & Giovanni Zilli, 2007. "Inexact constraint preconditioners for linear systems arising in interior point methods," Computational Optimization and Applications, Springer, vol. 36(2), pages 137-147, April.

    More about this item

    Keywords

    LINEAR PROGRAMMING; MATHEMATICS;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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