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.


Volume 9, Issue 2
April 2021
Pages 347-357
  • Receive Date: 05 December 2018
  • Revise Date: 03 October 2019
  • Accept Date: 10 October 2019
  • First Publish Date: 01 April 2021