  We explore the dual approach to nonlocal optimal design, specifically for a
classical min-max problem which in this study is associated with a nonlocal
scalar diffusion equation. We reformulate the optimal design problem utilizing
a dual variational principle, which is expressed in terms of nonlocal two-point
fluxes. We introduce the proper functional space framework to deal with this
formulation, and establish its well-posedness. The key ingredient is the
inf-sup (Ladyzhenskaya--Babuska--Brezzi) condition, which holds uniformly with
respect to small nonlocal horizons. As a byproduct of this, we are able to
prove convergence of nonlocal to local optimal design problems in a
straightforward fashion.
