Abstract
This short paper illustrates by examples and counterexamples the relative importance of some assumptions in recent results concerning the continuity and the directional differentiability of the optimal value function in a nonlinear programming problem.
This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-9273.
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References
A.V. Fiacco, W.P. Hutzler, “Extension of the Gauvin-Tolle optimal value differential stability results to general mathematical programs”, T-393, Institute for Management Science and Engineering, The George Washington University, Washington, DC (April 1979).
J. Gauvin and F. Dubeau, “Differential properties of the marginal function in mathematical programming”, Mathematical Programming Study 19 (1982) 101–119.
J. Gauvin, J.W. Tolle, “Differential stability in nonlinear programming”, SIAM Journal on Control and Optimization 15 (1977) 294–311.
R.T. Rockafellar, “Directional differentiability of the optimal value function in a nonlinear programming problem”, Mathematical Programming Study (to appear).
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© 1984 The Mathematical Programming Society, Inc.
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Gauvin, J., Dubeau, F. (1984). Some examples and counterexamples for the stability analysis of nonlinear programming problems. In: Fiacco, A.V. (eds) Sensitivity, Stability and Parametric Analysis. Mathematical Programming Studies, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121211
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DOI: https://doi.org/10.1007/BFb0121211
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