Abstract
This paper continues the local analysis of nonlinear programming problems begun in Parts I and II. In this part we exploit the tools developed in the earlier parts to obtain detailed information about local optimizers in the nondegenerate case. We show, for example, that these optimizers obey a weak type of differentiability and we compute their derivatives in this weak sense.
Sponsored by the National Science Foundation under Grant MCS 8200632, Mod. 2.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J.-P. Aubin, “Lipschitz behavior of solutions to convex minimization problems”, Mathematics of Operations Research 9 (1984) 87–111.
B. Cornet and G. Laroque, “Lipschitz properties of solutions in mathematical programming”, Discussion Paper 8321, Center for Operations Research and Econometrics (Louvain-la-Neuve, Belgium, 1983).
K. Jittorntrum, “Solution point differentiability without strict complementarity in mathematical programming”, Mathematical Programming Study 21 (1984) 127–138.
M. Kojima, “Strongly stable stationary solutions in nonlinear programs”, in: S.M. Robinson, ed., Analysis and computation of fixed points (Academic Press, New York, 1980) pp. 93–138.
G.P. McCormick, Nonlinear programming (Wiley-Interscience, New York, 1983).
S.M. Robinson, “Strongly regular generalized equations”, Mathematics of Operations Research 5 (1980) 43–62.
S.M. Robinson, “Some continuity properties of polyhedral multifunctions”, Mathematical Programming Study 14 (1981) 206–214.
S.M. Robinson, “Generalized equations,” in: A. Bachem, M. Grötschel and B. Korte, eds., Mathematical programming: The state of the art, Bonn 1982 (Springer-Verlag, Berlin, 1983) pp. 346–367.
S.M. Robinson, “Local structure of feasible sets in nonlinear programming, Part I: Regularity”, in: V. Pereyra and A. Reinoza, eds., Numerical methods (Springer-Verlag, Berlin, 1983) pp. 240–251.
S.M. Robinson, “Local structure of feasible sets in nonlinear programming, Part II: Nondegeneracy,” Mathematical Programming Study 22 (1984) 217–230.
R.T. Rockafellar, Convex analysis (Princeton University Press, Princeton, NJ, 1970).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 The Mathematical Programming Society, Inc.
About this chapter
Cite this chapter
Robinson, S.M. (1987). Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity. In: Cornet, B., Nguyen, V.H., Vial, J.P. (eds) Nonlinear Analysis and Optimization. Mathematical Programming Studies, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121154
Download citation
DOI: https://doi.org/10.1007/BFb0121154
Received:
Revised:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00930-3
Online ISBN: 978-3-642-00931-0
eBook Packages: Springer Book Archive