Characterizing Invex and Related Properties

  • B. D. Craven
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 77)


A characterization of invex, given by Glover and Craven, is extended to functions in abstract spaces. Pseudoinvex for a vector function coincides with invex in a restricted set of directions. The V-invex property of Jeyakumar and Mond is also characterized. Some differentiability properties of the invex scale function are also obtained.


Invexity Pseudoinvexity V-invex and necessary Lagrangian conditions 


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  1. Craven, B. D. and Glover, B. M. (1985), Invex functions and duality, Journal of the Australian Mathematical Society, Series A, Vol. 39, pp 1–20.MathSciNetCrossRefzbMATHGoogle Scholar
  2. V. Jeyakumar and B. Mond (1992), On generalized convex mathematical programming, Journal of the Australian Mathematical Society, Series B, Vol. 34, pp 43–53.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Craven, B. D. (2001), Vector generalized invex, Opsearch, Vol. 38, no. 4, pp 345–361.MathSciNetzbMATHGoogle Scholar
  4. Craven, B. D. (2002), Global invexity and duality in mathematical programming, Asia-Pacific Journal of Operational Research, Vol. 19, pp 169–175.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • B. D. Craven
    • 1
  1. 1.Dept of MathematicsUniversity of MelbourneAustralia

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