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In this paperwe consider a nonsmooth optimization problem with equality,
inequality and set constraints. We propose new constraint qualifications
and KuhnâTucker 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 MangasarianâFromovitz constraint qualification and show that this
constraint qualification is necessary and sufficient for the KuhnâTucker
multipliers set to be nonempty and bounded.
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