We present a determination of the local (z ≈ 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 < ∼ 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 Hα and Hβ 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 > ∼ M B J > ∼ −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 Hα 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 −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.