Mathematical Methods of Operations Research

, Volume 43, Issue 3, pp 319–336 | Cite as

Strengthened invex and perturbations

  • Bruce Desmond Craven
  • Do Van Luu
  • Bevil Milton Glover


If the strengthened invex property holds for a constrained minimization problem, then a Karush-Kuhn-Tucker point is a strict minimum. The strict minimum property is preserved under small perturbations of the problem. This allows sufficient conditions to be given for a minimax, starting from Karush-Kuhn-Tucker conditions. They extend to vector-valued minimax and to nonsmooth (Lipschitz) problems. An example is provided to illustrate the strengthened invex property, also a discussion of quadratic-linear (nonconvex) programming implications.

Key words

Strict constrained minimum strengthened invexity stability to perturbations minimax nonsmooth analysis 


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Copyright information

© Physica-Verlag 1996

Authors and Affiliations

  • Bruce Desmond Craven
    • 1
  • Do Van Luu
    • 2
  • Bevil Milton Glover
    • 3
  1. 1.Mathematics DepartmentUniversity of MelbourneParkvilleAustralia
  2. 2.Institute of Mathematics, HanoiBo Ho, HanoiVietnam
  3. 3.School of Information Technology and Mathematical SciencesUniversity of BallaratBallaratAustralia

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