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  • Bulletin of the Australian Mathematical Society, Volume 24, Issue 3
  • December 1981, pp. 357-366

Invex functions and constrained local minima

  • B.D. Craven (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700004895
  • Published online: 01 April 2009
Abstract

If a certain weakening of convexity holds for the objective and all constraint functions in a nonconvex constrained minimization problem, Hanson showed that the Kuhn-Tucker necessary conditions are sufficient for a minimum. This property is now generalized to a property, called K-invex, of a vector function in relation to a convex cone K. Necessary conditions and sufficient conditions are obtained for a function f to be K-invex. This leads to a new second order sufficient condition for a constrained minimum.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]B.D. Craven , Mathematical programming and control theory (Chapman and Hall, London; John Wiley & Sons, New York; 1978).

[5]Morgan A. Hanson , “On sufficiency of the Kuhn-Tucker conditions”, J. Math. Anal. Appl. 80 (1981), 545550.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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