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Sensitivity Analysis in (Degenerate) Quadratic Programming

Author

Listed:
  • Berkelaar, A.B.
  • Jansen, B.
  • Roos, K.
  • Terlaky, T.

Abstract

In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a right--hand side element (or an element of the linear part of the objective) is piecewise quadratic, where the pieces can be characterized by maximal complementary solutions and tripartitions. Further, we investigate differentiability of this function. A new algorithm to compute the optimal value function is proposed. Finally, we discuss the advantages of this approach when applied to mean--variance portfolio models.

Suggested Citation

  • 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.
    • Handle: RePEc:ems:eureir:1375
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    Cited by:

    1. 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.
    2. Haibing Lu & Jaideep Vaidya & Vijayalakshmi Atluri & Yingjiu Li, 2015. "Statistical Database Auditing Without Query Denial Threat," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 20-34, February.
    3. 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.

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