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Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization

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  • E. A. Yildirim

    (Stony Brook University)

Abstract

We study convex conic optimization problems in which the right-hand side and the cost vectors vary linearly as functions of a scalar parameter. We present a unifying geometric framework that subsumes the concept of the optimal partition in linear programming (LP) and semidefinite programming (SDP) and extends it to conic optimization. Similar to the optimal partition approach to sensitivity analysis in LP and SDP, the range of perturbations for which the optimal partition remains constant can be computed by solving two conic optimization problems. Under a weaker notion of nondegeneracy, this range is simply given by a minimum ratio test. We discuss briefly the properties of the optimal value function under such perturbations.

Suggested Citation

  • E. A. Yildirim, 2004. "Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 405-423, August.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:2:d:10.1023_b:jota.0000042528.76868.22
    DOI: 10.1023/B:JOTA.0000042528.76868.22
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    References listed on IDEAS

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    1. 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.
    2. Caron, Richard J. & Greenberg, Harvey J. & Holder, Allen G., 2002. "Analytic centers and repelling inequalities," European Journal of Operational Research, Elsevier, vol. 143(2), pages 268-290, December.
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    Cited by:

    1. M. A. Goberna & T. Terlaky & M. I. Todorov, 2010. "Sensitivity Analysis in Linear Semi-Infinite Programming via Partitions," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 14-26, February.
    2. Nguyen Ngoc Luan & Do Sang Kim & Nguyen Dong Yen, 2022. "Two Optimal Value Functions in Parametric Conic Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 574-597, June.

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