Journal of the Australian Mathematical Society (Series A)

Research Article

Invex functions and duality

B. D. Cravena1 and B. M. Glovera1

a1 Department of Mathematics University of Melbourne Parkville, Victoria 3052, Australia


For both differentiable and nondifferentiable functions defined in abstract spaces we characterize the generalized convex property, here called cone-invexity, in terms of Lagrange multipliers. Several classes of such functions are given. In addition an extended Kuhn-Tucker type optimality condition and a duality result are obtained for quasidifferentiable programming problems.

(Received January 25 1983)

(Revised June 18 1983)

1980 Mathematics subject classification (Amer. Math. Soc.)

  • 90 C 30