We initiate the study of the complexity-theoretic properties of convex logics in team semantics. We focus on the extension of classical propositional logic with the nonemptiness atom \( \textsc {ne}\) , a logic known to be both convex and union closed. We show that the satisfiability problem for this logic is \(\textrm{NP}\) -complete, that its validity problem is \(\textrm{coNP}\) -complete, and that its model-checking problem is in \(\textrm{P}\) .