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

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.

کلیدواژه ها:

Stationary conditions ، Vanishing constraints ، Nonsmooth optimization ، Constraint qualification