We present a determination of the local (z approximate to 0) luminosity function of optically selected type 1 (broad-line) active galactic nuclei. Our primary resource is the Hamburg/ESO survey (HES), which provides a well-defined sample of more than 300 optically bright AGN with redshifts z < 0.3 and blue magnitudes B less than or similar to 17.5. AGN luminosities were estimated in two ways, always taking care to minimise photometric biases due to host galaxy light contamination. Firstly, we measured broad-band B(J) (blue) magnitudes of the objects over small apertures of the size of the seeing disk. Secondly, we extracted H alpha and H beta broad emission line luminosities from the spectra which should be entirely free of any starlight contribution. Within the luminosity range covered by the HES (-19 greater than or similar to M(BJ) greater than or similar to -26), the two measures are tightly correlated. The resulting AGN luminosity function (AGNLF) is consistent with a single power law, also when considering the effects of number density evolution within the narrow redshift range. We compared our AGNLF with the Ha luminosity function of lower luminosity Seyfert 1 galaxies by Hao et al. (2005a, AJ, 129, 1795) and found a smooth transition between both, with excellent agreement in the overlapping region. From the combination of HES and SDSS samples we constructed a single local AGNLF spanning more than 4 orders of magnitude in luminosity. It shows only mild curvature which can be well described as a double power law with slope indices of -2.0 for the faint end and -2.8 for the bright end. We predicted the local AGNLF in the soft X-ray domain and compared this to recent literature data. The quality of the match depends strongly on the adopted translation of optical to X-ray luminosities and is best for an approximately constant optical/X-ray ratio. We also compared the local AGNLF with results obtained at higher redshifts and find strong evidence for luminosity-dependent evolution, in the sense that AGN with luminosities around M(B) similar or equal to -19 are as common in the local universe as they were at z = 1.5. This supports the "AGN downsizing" picture first found from X-ray selected AGN samples.
