The problem is $$ \sup_{\delta\in\mathcal{N}_0}(w^\top \delta), $$ where $\mathcal{N}_0=\{\delta|||\delta||^*\leq c\}$ with $||\cdot||^*$ being the dual norm for an arbitrary norm.
The conclusion in a paper says the result is $c||w||$. But I don't know how to derive this result. Thanks a lot to anyone who can tell me how to deal with this kind of optimization problems with dual norms.