Land use planning problem: a primal-dual splitting algorithm

We propose a convex optimization urban planning problem for a wide class of objective functions. The dual of this problem is computed and the existence and uniqueness of the primal-dual solution are guaranteed under suitable conditions. A convergent algorithm is proposed, which solves the primal and dual problems simultaneously. Finally, our framework is illustrated by an application for the case where the planning goal is to attain spatial socio-economic homogeneity and numerical simulations are implemented.