  The inclusion of nucleonic exchange energy has been a long-standing challenge
for the relativistic density functional theory (RDFT) in nuclear physics. We
propose an orbital-dependent relativistic Kohn-Sham density functional theory
to incorporate the exchange energy with local Lorentz scalar and vector
potentials. The relativistic optimized effective potential equations for the
local exchange potentials are derived and solved efficiently. The obtained
binding energies and charge radii for nuclei are benchmarked with the results
given by the traditional relativistic Hartree-Fock approach, which involves
complicated nonlocal potentials. It demonstrates that the present framework is
not only accurate but also efficient.
