Extensions of the Kuhn--Tucker Constraint Qualification to Generalized Semi-infinite Programming

  • Authors:

  • Francisco Guerra Vázquez;Jan-J. Rückmann

  • Affiliations:

  • -;-

  • Venue:
  • SIAM Journal on Optimization
  • Year:
  • 2005

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Abstract

This paper deals with the class of generalized semi-infinite programming problems (GSIPs) in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be continuously differentiable. We introduce two extensions of the Kuhn--Tucker constraint qualification (which is based on the existence of a tangential continuously differentiable arc) to the class of GSIPs, prove a corresponding Karush--Kuhn--Tucker theorem, and discuss its assumptions. Finally, we present several examples which illustrate for the class of GSIPs some interrelations between the considered extensions of the Mangasarian--Fromovitz constraint qualification, the Abadie constraint qualification, and the Kuhn--Tucker constraint qualification.