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The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming

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  • Berkelaar, A.B.
  • Roos, K.
  • Terlaky, T.

Abstract

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach (using optimal bases) is shown. Moreover, we present an algorithm to compute the partitions, optimal sets and the optimal value function. This is a new algorithm and uses primal and dual optimal solutions. We also extend some of the results to parametric quadratic programming, and discuss differences and resemblances with the linear programming case.

Suggested Citation

  • 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.
    • Handle: RePEc:ems:eureir:1394
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    References listed on IDEAS

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    1. Voros, J., 1987. "The explicit derivation of the efficient portfolio frontier in the case of degeneracy and general singularity," European Journal of Operational Research, Elsevier, vol. 32(2), pages 302-310, November.
    2. Berkelaar, A.B. & Jansen, B. & Roos, K. & Terlaky, T., 1996. "Sensitivity Analysis in (Degenerate) Quadratic Programming," Econometric Institute Research Papers EI 9611-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Voros, J., 1986. "Portfolio analysis--an analytic derivation of the efficient portfolio frontier," European Journal of Operational Research, Elsevier, vol. 23(3), pages 294-300, March.
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    Cited by:

    1. 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.
    2. 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.

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