Hi Igor, currently there isn't a search built into the API. In fact, in the 11+ years the API has been around, this is the first time I've heard a request for that. It's a great idea, and one I think would be beneficial to the users, but it's not in there now. I'd suggest you put an enhancement request in with your support channel to work on getting it put in.
With that said, making a get_list() call with 11k objects should still work. You'll likely want to split that list down when calling subsequent functions with that listing thought.
-Joe