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For exchange-correlation functionals that depend explicitly on the Kohn-Shamorbitals, the potential $V_{\mathrm{xc}\sigma}(\re)$ must be obtained as thesolution of the optimized effective potential (OEP) integral equation. This isvery demanding and has limited the use of orbital functionals like exactexchange. We demonstrate that the OEP can be obtained iteratively by solving asystem of partial differential equations instead of an integral equation. Thisamounts to calculating the orbital shifts that exactify the Krieger-Li-Iafrate(KLI) approximation. Unoccupied orbitals do not need to be calculated. Accuracyand efficiency of the method are shown for atoms and clusters using the exactexchange energy. Counter-intuitive asymptotic limits of the exact OEP, notaccessible from previous constructions, are presented.Comment: Physical Review Letters, accepted for publication. 4 pages, 1 figur

Simple Iterative Construction of the Optimized Effective Potential for Orbital Functionals, Including Exact Exchange