Abstract
Regarding a special class of convex parametric problems sufficient conditions for the lower semicontinuity of the optimal solution sets are developed.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
C. Berge, Topological spaces (Macmillan, New York, 1963).
G.B. Dantzig, J. Folkman and N. Shapiro, “On the continuity of the minimum set of a continuous function”, Journal of Mathematical Analysis and Applications 17 (1967) 519–548.
G. Debreu, Theory of value (John Wiley, New York, 1959).
J.P. Evans and F.J. Gould, “Stability in nonlinear programming”, Operations Research 18 (1970) 107–118.
H.J. Greenberg and W.P. Pierskalla, “Extensions of the Evans-Gould stability theorems for mathematical programs”, Operations Research 20 (1972) 143–153.
J. Guddal, “Stability in convex quadratic parametric programming”, Mathematische Operations forschung und Statistik 7 (1976) 223–245.
J. Guddat and D. Klatte. “Qualitative stability in nonlinear optimization”, Proceedings of the IX. Internat. Symposium on Mathematical Programming, Budapest, 1976 (to appear).
W.W. Hogan, “Point-to-set maps in mathematical programming”, SIAM Review 15 (1973) 591–603.
P. Huard, “Optimization algorithms and point-to-set maps”, Mathematical Programming 8 (1975) 308–331.
D. Klatte, “Untersuchungen zur lokalen Stabilität konvexer parametrischer Optimierungsprobleme”, Dissertation (A), (Humboldt-Universität, Berlin, 1977).
B. Kummer, “Stability and weak duality in convex programming without regularity”, preprint (Humboldt-Universität, Berlin, 1978).
R. Meyer, “The validity of a family of optimization methods”, SIAM Journal on Control 8 (1970) 41–54.
F. Nožička, J. Guddat, H. Hollatz und B. Bank, Theorie der linearen parametrischen Optimierung (Akademie-Verlag, Berlin, 1974).
S.M. Robinson and R.H. Day, “A sufficient condition for continuity of optimal sets in mathematical programming”, Journal, of Mathematical Analysis and Application 45 (1974) 506–511.
R.T. Rockafellar, Convex analysis (Princeton University Press, Princeton, NJ, 1970).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 The Mathematical Programming Society
About this chapter
Cite this chapter
Klatte, D. (1979). On the lower semicontinuity of optimal sets in convex parametric optimization. In: Huard, P. (eds) Point-to-Set Maps and Mathematical Programming. Mathematical Programming Studies, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120847
Download citation
DOI: https://doi.org/10.1007/BFb0120847
Received:
Revised:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00797-2
Online ISBN: 978-3-642-00798-9
eBook Packages: Springer Book Archive