Hostname: page-component-6bf8c574d5-w79xw Total loading time: 0 Render date: 2025-02-26T15:10:16.090Z Has data issue: false hasContentIssue false
  • English
  • Français

Sufficient Fritz John optimality conditions

Published online by Cambridge University Press:  17 April 2009

B.D. Craven
B.D. Craven
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
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.

The sufficient optimality conditions, of Fritz John type, given by Gulati for finite-dimensional nonlinear programming problems involving polyhedral cones, are extended to problems with arbitrary cones and spaces of arbitrary dimension, whether real or complex. Convexity restrictions on the function giving the equality constraint can be avoided by applying a modified notion of convexity to the other functions in the problem. This approach regards the problem as optimizing on a differentiable manifold, and transforms the problem to a locally equivalent one where the optimization is on a linear subspace.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 3 , December 1975 , pp. 411 - 419
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]Craven, B.D., “A generalization of Lagrange multipliers”, Bull. Austral. Math. Soc. 3 (1970), 353–362.CrossRefGoogle Scholar
[3]Craven, B.D., “Converse duality in Banach space”, J. Optimization Theory Appl. 17 (1975), 229–238.CrossRefGoogle Scholar
[4]Craven, B.D., “A generalized Motzkin alternative theorem” (Research Report, 13. School of Mathematical Sciences, University of Melbourne, Parkville, 1975).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., “Transposition theorems for cone-convex functions”, SIAM J. Appl. Math. 24 (1973), 603–612.CrossRefGoogle Scholar
[7]Craven, B.D. and Mond, B., “Real and complex Fritz John theorems”, J. Math. Anal. Appl. 44 (1973), 773–778.CrossRefGoogle Scholar
[8]Craven, B.D. and Mond, B., “A Fritz John theorem in complex space”, Bull. Austral. Math. Soc. 8 (1973), 215–220.CrossRefGoogle Scholar
[9]Gulati, T.R., “A Fritz John type sufficient optimality theorem in complex space”, Bull. Austral. Math. Soc. 11 (1974), 219–224.CrossRefGoogle Scholar