The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

What is invexity?

A. Ben-Israela1 and B. Monda2

a1 Department of Mathematical Science, University of Delaware, Newark, DE 19716, U.S.A.

a2 Department of Mathematical, La Trobe University, Bundoor, Vic. 3083, Australia.


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.

(Received February 08 1985)

(Revised May 28 1985)