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Sensitivity analysis in optimization and reliability problems

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  • Castillo, Enrique
  • Mínguez, Roberto
  • Castillo, Carmen

Abstract

The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods.

Suggested Citation

  • Castillo, Enrique & Mínguez, Roberto & Castillo, Carmen, 2008. "Sensitivity analysis in optimization and reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1788-1800.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:12:p:1788-1800
    DOI: 10.1016/j.ress.2008.03.010
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    References listed on IDEAS

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    1. E. Castillo & A. Conejo & C. Castillo & R. Mínguez, 2007. "Closed formulas in local sensitivity analysis for some classes of linear and non-linear problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 355-371, December.
    2. E. Castillo & A. J. Conejo & C. Castillo & R. Mínguez & D. Ortigosa, 2006. "Perturbation Approach to Sensitivity Analysis in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 49-74, January.
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    Citations

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    Cited by:

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    2. Li, Luyi & Lu, Zhenzhou & Hu, JiXiang, 2014. "A new kind of regional importance measure of the input variable and its state dependent parameter solution," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 1-16.
    3. Li, Luyi & Lu, Zhenzhou, 2013. "Importance analysis for models with correlated variables and its sparse grid solution," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 207-217.
    4. Kim, Taeyong & Song, Junho, 2018. "Generalized Reliability Importance Measure (GRIM) using Gaussian mixture," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 105-115.
    5. Zhai, Qingqing & Yang, Jun & Xie, Min & Zhao, Yu, 2014. "Generalized moment-independent importance measures based on Minkowski distance," European Journal of Operational Research, Elsevier, vol. 239(2), pages 449-455.
    6. Sobey, A.J. & Blake, J.I.R. & Shenoi, R.A., 2013. "Monte Carlo reliability analysis of tophat stiffened composite plate structures under out of plane loading," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 41-49.
    7. Michael K. McWilliam & Antariksh C. Dicholkar & Frederik Zahle & Taeseong Kim, 2022. "Post-Optimum Sensitivity Analysis with Automatically Tuned Numerical Gradients Applied to Swept Wind Turbine Blades," Energies, MDPI, vol. 15(9), pages 1-19, April.
    8. Hao, Wenrui & Lu, Zhenzhou & Tian, Longfei, 2012. "Importance measure of correlated normal variables and its sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 151-160.
    9. Hao, Wenrui & Lu, Zhenzhou & Wei, Pengfei, 2013. "Uncertainty importance measure for models with correlated normal variables," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 48-58.
    10. Luyi Li & Zhenzhou Lu, 2016. "A new algorithm for importance analysis of the inputs with distribution parameter uncertainty," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(13), pages 3065-3077, October.
    11. Zhang, Xufang & Pandey, Mahesh D., 2014. "An effective approximation for variance-based global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 164-174.
    12. Yishang Zhang & Yongshou Liu & Xufeng Yang & Bin Zhao, 2015. "An efficient Kriging method for global sensitivity of structural reliability analysis with non-probabilistic convex model," Journal of Risk and Reliability, , vol. 229(5), pages 442-455, October.

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