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Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

Author

Listed:
  • F. García

    (Universidad de Alicante)

  • M. A. Melguizo Padial

    (Universidad de Alicante)

Abstract

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.

Suggested Citation

  • F. García & M. A. Melguizo Padial, 2015. "Sensitivity Analysis in Convex Optimization through the Circatangent Derivative," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 420-438, May.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0609-4
    DOI: 10.1007/s10957-014-0609-4
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    References listed on IDEAS

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    1. T. D. Chuong & J. C. Yao, 2010. "Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 77-94, July.
    2. Hansen, Pierre & Labbe, Martine & Wendell, Richard E., 1989. "Sensitivity analysis in multiple objective linear programming: The tolerance approach," European Journal of Operational Research, Elsevier, vol. 38(1), pages 63-69, January.
    3. Balbas, A. & Ballve, M. & Jimenez Guerra, P., 2001. "Density theorems for ideal points in vector optimization," European Journal of Operational Research, Elsevier, vol. 133(2), pages 260-266, January.
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