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A Tutorial on Sensitivity and Stability in Nonlinear Programming and Variational Inequalities under Differentiability Assumptions

Author

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  • Giorgio

    (Department of Economics and Management, University of Pavia)

  • Cesare

    (Department of Economics and Management, University of Pavia)

Abstract

In this paper basic results on sensitivity and stability analysis in differentiable nonlinear programming problems are surveyed. We follow mainly the approach of A. V. Fiacco and his co-authors. We give also an overview on sensitivity for right-hand side perturbations of the parameters, on sensitivity for parametric linear programming problems and on sensitivity for parametric variational inequality problems.

Suggested Citation

  • Giorgio & Cesare, 2018. "A Tutorial on Sensitivity and Stability in Nonlinear Programming and Variational Inequalities under Differentiability Assumptions," DEM Working Papers Series 159, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0159
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0159.pdf
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    References listed on IDEAS

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    1. Jacques Gauvin, 1979. "The Generalized Gradient of a Marginal Function in Mathematical Programming," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 458-463, November.
    2. D. Gale, 1967. "A Geometric Duality Theorem with Economic Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 19-24.
    3. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985.
    4. Jansen, B. & de Jong, J. J. & Roos, C. & Terlaky, T., 1997. "Sensitivity analysis in linear programming: just be careful!," European Journal of Operational Research, Elsevier, vol. 101(1), pages 15-28, August.
    5. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, September.
    6. Harvey J. Greenberg & William P. Pierskalla, 1972. "Extensions of the Evans-Gould Stability Theorems for Mathematical Programs," Operations Research, INFORMS, vol. 20(1), pages 143-153, February.
    7. M. L. Balinski & W. J. Baumol, 1968. "The Dual in Nonlinear Programming and its Economic Interpretation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(3), pages 237-256.
    8. A. L. Soyster, 1981. "Note---An Objective Function Perturbation with Economic Interpretations," Management Science, INFORMS, vol. 27(2), pages 231-237, February.
    9. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    10. J. P. Evans & F. J. Gould, 1970. "Stability in Nonlinear Programming," Operations Research, INFORMS, vol. 18(1), pages 107-118, February.
    11. M. Seetharama Gowda & Jong-Shi Pang, 1994. "Stability Analysis of Variational Inequalities and Nonlinear Complementarity Problems, via the Mixed Linear Complementarity Problem and Degree Theory," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 831-879, November.
    12. Stephen M. Robinson, 1977. "A Characterization of Stability in Linear Programming," Operations Research, INFORMS, vol. 25(3), pages 435-447, June.
    13. Michael H. Stern & Donald M. Topkis, 1976. "Rates of Stability in Nonlinear Programming," Operations Research, INFORMS, vol. 24(3), pages 462-476, June.
    14. Vadim Bondarevsky & Alexey Leschov & Leonid Minchenko, 2016. "Value Functions and Their Directional Derivatives in Parametric Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 440-464, November.
    15. Yuping Qiu & Thomas L. Magnanti, 1992. "Sensitivity Analysis for Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 61-76, February.
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    Cited by:

    1. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.

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