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A Fritz John theorem in complex space

Published online by Cambridge University Press:  17 April 2009

B.D. Craven  and
B. Mond
B.D. Craven
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria;
B. Mond
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria.
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Abstract

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Necessary conditions of the Fritz John type are given for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space.

Consider the problem to

where S is a polyhedral cone in, and Cm and f: C2n → C, g : C2n → Cm are differentiable functions. A necessary condition for a feasible point z0 to be optimal is that there exist τ≥0, ν ∈ S*, (τ, ν) ≠ 0, such that

and

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 2 , April 1973 , pp. 215 - 220
Copyright
Copyright © Australian Mathematical Society 1973

References

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