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Invex functions and constrained local minima

Published online by Cambridge University Press:  17 April 2009

B.D. Craven
B.D. Craven
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia.
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Abstract

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If a certain weakening of convexity holds for the objective and all constraint functions in a nonconvex constrained minimization problem, Hanson showed that the Kuhn-Tucker necessary conditions are sufficient for a minimum. This property is now generalized to a property, called K-invex, of a vector function in relation to a convex cone K. Necessary conditions and sufficient conditions are obtained for a function f to be K-invex. This leads to a new second order sufficient condition for a constrained minimum.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 3 , December 1981 , pp. 357 - 366
Copyright
Copyright © Australian Mathematical Society 1981

References

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