Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-09-17T21:34:04.546Z Has data issue: false hasContentIssue false
  • English
  • Français

Necessary conditions for a mathematical programming problem with set and cone constraints

Published online by Cambridge University Press:  17 February 2009

Youji Nagahisa
Youji Nagahisa
Affiliation:
Department of Mathematics, Faculty of Education, Yamaguchi University, Yosida, Yamaguchi, 753, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is devoted to the derivation of a necessary condition of F. John type which must be satisfied by a solution of a mathematical programming problem with set and cone constraints. The necessary condition is applied to an optimisation problem defined on functional spaces with inequality state constraints. Furthermore a pseudo open mapping theorem is developed in the course of proving the main theorem.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 3 , January 1988 , pp. 310 - 321
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bender, P. J., “Nonlinear programming in normed linear spaces”, J. Optim. Theory Appl. 24 (1978) 263–285.CrossRefGoogle Scholar
[2]Borwein, J., “Weak tangent cones and optimization in a Banach space”, SIAM J. Control Optim. 16 (1978) 512–522.Google Scholar
[3]Craven, B. D., “Lagrangean conditions and quasiduality”, Bull. Austral. Math. Soc. 16 (1977) 325–339.CrossRefGoogle Scholar
[4]Dunford, N. and Schwartz, J. T., Linear operators Part I: General theory (Interscience, New York, 1964).Google Scholar
[5]Holmes, R. B., Geometric functional analysis and its applications (Springer-Verlag, New York, 1975).CrossRefGoogle Scholar
[6]Kurcyusz, S., “On the existence and nonexistence of Lagrange multipliers in Banach spaces”, J. Optim. Theory Appl. 20 (1976) 81–110.CrossRefGoogle Scholar
[7]Nagahisa, Y. and Sakawa, Y., “Nonlinear programming in Banach spaces”, J. Optim. Theory Appl. 4 (1969) 182–190.CrossRefGoogle Scholar
[8]Varaiya, P. P., “Nonlinear programming in Banach space”, SIAM J. Appl. Math. 15 (1957) 284–293.CrossRefGoogle Scholar
[9]Zowe, J. and Kurcyusz, S., “Regularity and stability for the mathematical programming in Banach spaces”, Appl. Math. Opt. 5 (1979) 49–64.Google Scholar