A numerical iteration scheme is presented for the calculation of coherent vortex structures. Steady solutions of the Euler vorticity equation are found, using a variational characterization for dipolar and monopolar vortices as relative equilibria of the Poisson system. The variational principle for the vorticity is solved by a numerical method for nonconvex optimization. Besides the variational principle for the vorticity, an optimization process is used for the multipliers that appear in the description. The free boundary is solved implicitly in the iteration process.