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What is invexity?

Published online by Cambridge University Press:  17 February 2009

A. Ben-Israel  and
B. Mond
A. Ben-Israel
Affiliation:
Department of Mathematical Science, University of Delaware, Newark, DE 19716, U.S.A.
B. Mond
Affiliation:
Department of Mathematical, La Trobe University, Bundoor, Vic. 3083, Australia.
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Abstract

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Recently it was shown that many results in Mathematical Programming involving convex functions actually hold for a wider class of functions, called invex. Here a simple characterization of invexity is given for both constrained and unconstrained problems. The relationship between invexity and other generalizations of convexity is illustrated. Finally, it is shown that invexity can be substituted for convexity in the saddle point problem and in the Slater constraint qualification.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 1 , July 1986 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 1986

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