Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints

Document Type : Research Paper


Department of Mathematics, Payam Noor University, P. O. Box 19395-3697, 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.