University of Tabriz Computational Methods for Differential Equations 2345-3982 9 2 2021 04 01 Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints 347 357 10352 10.22034/cmde.2020.30733.1459 EN Hadis Mokhtavayi Department of Mathematics, Payam Noor University, P. O. Box 19395-3697, Tehran, Iran. Aghileh Heidari Department of Mathematics, Payam Noor University, P. O. Box 19395-3697, Tehran, Iran. Nader Kanzi Department of Mathematics, Payam Noor University, P. O. Box 19395-3697, Tehran, Iran. Journal Article 2018 12 05 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 https://cmde.tabrizu.ac.ir/article_10352_0b6a2959c2b43ba7461b1c2201c089da.pdf