As far as I know, you can't do this in the web interface yet. So if you want to do it in the interface, you'll need to write a module or workflow event type.
That's what I thought at the beginning, but then I needed to sort the articles based on this date. I didn't want to go through a custom fetch and wanted to use the standard sort features (eg. on the "what's new page"), that's why I needed to change the publication date.
Beside, as a matter of principle, I don't like when the system sets something and the admin can't change it.