Hadis Mokhtavayi - Department of Mathematics, Payam Noor University, P. O. Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran.
Aghileh Heidari - Department of Mathematics, Payam Noor University, P. O. Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran.
Nader Kanzi - Department of Mathematics, Payam Noor University, P. O. Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran.

We consider a nonsmooth optimization problem with a feasible set defined by vanishing constraints. First, we introduce a constraint qualification for the problem, named NNAMCQ. Then, NNAMCQ is applied to obtain a necessary M-stationary condition. Finally, we present a sufficient condition for M-stationarity, under generalized convexity assumption. Our results are formulated in terms of Mordukhovich subdifferential.

Stationary conditions, Vanishing constraints, Nonsmooth optimization, Constraint qualification