  We present a new optimization-based method for atomistic-to-continuum (AtC)
coupling. The main idea is to cast the coupling of the atomistic and continuum
models as a constrained optimization problem with virtual Dirichlet controls on
the interfaces between the atomistic and continuum subdomains. The optimization
objective is to minimize the error between the atomistic and continuum
solutions on the overlap between the two subdomains, while the atomistic and
continuum force balance equations provide the constraints. Splitting of the
atomistic and continuum problems instead of blending them and their subsequent
use as constraints in the optimization problem distinguishes our approach from
the existing AtC formulations. We present and analyze the method in the context
of a one-dimensional chain of atoms modeled using a linearized two-body
next-nearest neighbor interactions.
