Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-24T06:13:24.421Z Has data issue: false hasContentIssue false
  • English
  • Français

On converse duality in complex nonlinear programming

Published online by Cambridge University Press:  17 April 2009

J. Parida
J. Parida
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela, Orissa, India.
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.

In this note a converse duality theorem is proved for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space by a direct use of a Kuhn-Tucker type necessary and sufficient condition for constrained optimization in complex space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 3 , December 1975 , pp. 421 - 427
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Abrams, Robert A., “Nonlinear programming in complex space: sufficient conditions and duality”, J. Math. Anal. Appl. 38 (1972), 619–632.CrossRefGoogle Scholar
[2]Abrams, Robert A. and Ben-Israel, Adi, “Nonlinear programming in complex space: necessary conditions”, SIAM J. Control 9 (1971), 606–620.CrossRefGoogle Scholar
[3]Abrams, Robert A., Ben-Israel, Adi, “Complex mathematical programming” (Report No. 69–11, Northwestern University, Evanston, Illinois, 1969).Google Scholar
[4]Bochner, Salomon and Martin, William Ted, Several complex variables (Princeton Mathematical Series, 10. Princeton University Press, Princeton, 1948).Google Scholar
[5]Craven, B.D. and Mond, B., “Converse and symmetric duality in complex nonlinear programming”, J. Math. Anal. Appl. 37 (1972), 617–626.CrossRefGoogle Scholar
[6]Craven, B.D. and Mond, B., “Real and complex Fritz John theorems”, J. Math. Anal. Appl. 44 (1973), 773–778.CrossRefGoogle Scholar
[7]Wolfe, P., “A duality theorem for non-linear programming”, Quart. Appl. Math. 19 (1961), 239–244.CrossRefGoogle Scholar