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A nonsmooth variant of the Mangasarian-Fromovitz constraint qualification

Abstract

A unified view on constraint qualifications for nonsmooth equality and inequality constrained programs is presented. A fairly general constraint qualification for programs involving B-differential functions is given. Further specification to piecewise differentiable equality constraints and locally Lipschitz continuous inequality constraints yields a nonsmooth version of the Mangasarian-Fromovitz constraint qualification.

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This work was supported by the Deutsche Forschungsgemeinschaft, DFG-Grant No. Pa 219/5-1.

Communicated by O. L. Mangasarian

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Kuntz, L., Scholtes, S. A nonsmooth variant of the Mangasarian-Fromovitz constraint qualification. J Optim Theory Appl 82, 59–75 (1994). https://doi.org/10.1007/BF02191779

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Key Words

  • Nonsmooth programming
  • constraint qualifications
  • B-differentiable functions
  • necessary optimality conditions
  • piecewise differentiable functions