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“School of Mathematics”

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Paper   IPM / M / 14989
School of Mathematics
  Title:   Convexificators and boundedness of the Kuhn-Tucker multipliers set
  Author(s):  Soghra Nobakhtian (Joint with A. Ansari Ardali and N. Movahedian)
  Status:   Published
  Journal: Optimization
  Vol.:  66
  Year:  2017
  Pages:   1445-1463
  Supported by:  IPM
  Abstract:
In this paperwe consider a nonsmooth optimization problem with equality, inequality and set constraints. We propose new constraint qualifications and Kuhn–Tucker type necessary optimality conditions for this problem involving locally Lipschitz functions. The main tool of our approach is the notion of convexificators. We introduce a nonsmooth version of the Mangasarian–Fromovitz constraint qualification and show that this constraint qualification is necessary and sufficient for the Kuhn–Tucker multipliers set to be nonempty and bounded.

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