In this paper, optimality conditions for the group sparse constrained optimization (GSCO) problems are studied. Firstly, equivalent characterizations of Bouligand tangent cone, Clarke cone and their corresponding normal cones set derived. Secondly, by using cones, four types stationary points GSCO given: TB-stationary point, NB-stationary TC-stationary point NC-stationary which used to characte...

in this paper we study optimization problems with infinite many inequality constraints on a banach space where the objective function and the binding constraints are locally lipschitz‎. ‎necessary optimality conditions and regularity conditions are given‎. ‎our approach are based on the michel-penot subdifferential.