  We present an Augmented Lagrangian formulation and its real-space
implementation for non-periodic orbital-free Density Functional Theory (OF-DFT)
calculations. In particular, we rewrite the constrained minimization problem of
OF-DFT as a sequence of minimization problems without any constraint, thereby
making it amenable to powerful unconstrained optimization algorithms. Further,
we develop a parallel implementation of this approach for the Thomas-Fermi-von
Weizscaker (TFW) kinetic energy functional in the framework of higher-order
finite-differences and the conjugate gradient method. With this implementation,
we establish that the Augmented Lagrangian approach is highly competitive
compared to the penalty and Lagrange multiplier methods. Additionally, we show
that higher-order finite-differences represent a computationally efficient
discretization for performing OF-DFT simulations. Overall, we demonstrate that
the proposed formulation and implementation is both efficient and robust by
studying selected examples, including systems consisting of thousands of atoms.
We validate the accuracy of the computed energies and forces by comparing them
with those obtained by existing plane-wave methods.
