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

نویسندگان
Mokhtavayi, Hadis ID 1
Heidari, Aghileh ID 2
Kanzi, Nader ID 3

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

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

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

doi
10.22034/cmde.2020.30733.1459
چکیده

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.

کلیدواژه‌ها
Stationary conditions, Vanishing constraints, Nonsmooth optimization, Constraint qualification