@article { author = {Mokhtavayi, Hadis and Heidari, Aghileh and Kanzi, Nader}, title = {Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints}, journal = {Computational Methods for Differential Equations}, volume = {9}, number = {2}, pages = {347-357}, year = {2021}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {10.22034/cmde.2020.30733.1459}, abstract = {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.}, keywords = {Stationary conditions,Vanishing constraints,Nonsmooth optimization,Constraint qualification}, url = {https://cmde.tabrizu.ac.ir/article_10352.html}, eprint = {https://cmde.tabrizu.ac.ir/article_10352_0b6a2959c2b43ba7461b1c2201c089da.pdf} }