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Analytic Central Path, Sensitivity Analysis and Parametric Linear Programming

Author

Listed:
  • A.G. Holder

    (University of Colorado at Denver)

  • J.F. Sturm

    (Erasmus University Rotterdam)

  • S. Zhang

    (Erasmus University Rotterdam)

Abstract

In this paper we consider properties of the central path and the analytic center of the optimalface in the context of parametric linear programming. We first show that if the right-hand sidevector of a standard linear program is perturbed, then the analytic center of the optimal face isone-side differentiable with respect to the perturbation parameter. In that case we also showthat the whole analytic central path shifts in a uniform fashion. When the objective vector isperturbed, we show that the last part of the analytic central pathis tangent to a central path defined on the optimal face of the original problem.

Suggested Citation

  • A.G. Holder & J.F. Sturm & S. Zhang, 1998. "Analytic Central Path, Sensitivity Analysis and Parametric Linear Programming," Tinbergen Institute Discussion Papers 98-003/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19980003
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    References listed on IDEAS

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    1. Michael J. Todd, 1990. "A Dantzig-Wolfe-Like Variant of Karmarkar's Interior-Point Linear Programming Algorithm," Operations Research, INFORMS, vol. 38(6), pages 1006-1018, December.
    2. Berkelaar, A.B. & Roos, K. & Terlaky, T., 1996. "The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming," Econometric Institute Research Papers EI 9658-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. J. Frédéric Bonnans & Florian A. Potra, 1997. "On the Convergence of the Iteration Sequence of Infeasible Path Following Algorithms for Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 378-407, May.
    4. Nunez, M. A. (Manuel A.) & Freund, Robert Michael. & Massachusetts Institute of Technology. Operations Research Center., 1996. "Condition measures and properties of the central trajectory of a linear program," Working papers 316-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1995. "A Surface of Analytic Centers and Primal-Dual Infeasible-Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 135-162, February.
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    Citations

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    Cited by:

    1. Zhang, S., 1998. "Global error bounds for convex conic problems," Econometric Institute Research Papers EI 9830, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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