  We propose a family of differential models for B-type open-closed topological
Landau-Ginzburg theories defined by a pair $(X,W)$, where $X$ is any
non-compact Calabi-Yau manifold and $W$ is any holomorphic complex-valued
function defined on $X$ whose critical set is compact. The models are
constructed at cochain level using smooth data, including the twisted Dolbeault
algebra of polyvector valued forms and a twisted Dolbeault category of
holomorphic factorizations of $W$. We give explicit proposals for cochain level
versions of the bulk and boundary traces and for the bulk-boundary and
boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the
axioms of an open-closed topological field theory are satisfied on cohomology
and conjecture that the remaining axioms are also satisfied.
