Abstract
A unified second order theory for extremum problems is applied to obtain second order necessary conditions for semi-infinite programming problems. The well known first order conditions are included. An application to the problem of best local nonlinear approximation is given.
Preview
Unable to display preview. Download preview PDF.
References
Ben-Tal, A., "Second order theory of extremum problems", Proceedings of the International Symposium on External Methods and System Analysis (Fiacco, A.V., Kortanek, K., Editors), University of Texas, Austin, 1977, (to appear).
Cheney, E., Introduction to approximation theory, McGraw Hill, New York, 1966.
Gehner, K.R., "Necessary and sufficient optimality conditions for the Fritz-John problem with linear equality constraints", SIAM J.Control,12,pp. 140–149.
Gehner, K.R., "Characterization theorems for constrained approximation problems via optimization theory", J. Approximation Theory, 14, pp.51–76 (1975).
Girsanov, I., Lectures on the Mathematical Theory of Extremum Problems, Lecture notes in Econ. and Math.Systems, #67 Springer Verlag, New-York, 1972.
Gustafson, S.A., Kortanek, K.O., "Numerical treatment of a class of semi-infinite programming problems", Nav.Res.log.Quar., 20(1973), pp.477–504).
Hettich, R.T., Jongen, A.Th., "Semi-infinite programming: Conditions of optimality and applications", Optimization Techniques (Stoer, J., Editor), Lecture Notes in Control and Information Sciences, Springer, 1978.
John, F., "Extremum problems with inequalities as subsidiary conditions", Studies and Essays, Courant Anniversary Volume, Interscience, New York, 1968, pp, 187–204.
Krabs, W., Optimierung und Approximation, Teubner, Stuttgart, 1975.
Laurent, J.P., Optimisation et Approximation, Herman, Paris, 1972
Pchenichnyi, B., Necessary conditions for an Extremum, Marcel Dekker, New York, 1970.
Rockafellar, R.T., Convex Analysis, Princeton University Press, Princeton, 1970.
Stoer, J., Witzgall, C., Convexity and Optimization in finite dimensions I., Springer, 1970.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Ben-Tal, A., Teboulle, M., Zowe, J. (1979). Second order necessary optimality conditions for semi-infinite programming problems. In: Hettich, R. (eds) Semi-Infinite Programming. Lecture Notes in Control and Information Sciences, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0003881
Download citation
DOI: https://doi.org/10.1007/BFb0003881
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09479-1
Online ISBN: 978-3-540-35213-6
eBook Packages: Springer Book Archive