  We present an optimization-based coupling method for local and nonlocal
continuum models. Our approach couches the coupling of the models into a
control problem where the states are the solutions of the nonlocal and local
equations, the objective is to minimize their mismatch on the overlap of the
local and nonlocal problem domains, and the virtual controls are the nonlocal
volume constraint and the local boundary condition. We present the method in
the context of Local-to-Nonlocal diffusion coupling. Numerical examples
illustrate the theoretical properties of the approach.
