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Analytic central path, sensitivity analysis and parametric linear programming

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  • Holder, A.G.
  • Sturm, J.F.
  • Zhang, S.

Abstract

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

Suggested Citation

  • Holder, A.G. & Sturm, J.F. & Zhang, S., 1998. "Analytic central path, sensitivity analysis and parametric linear programming," Econometric Institute Research Papers EI 9801, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1557
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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. 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.
    4. 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.
    5. 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.
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