As of v 0.7.0 of the private registry you can do:
$ curl -X GET http://localhost:5000/v1/search?q=postgresql
and you will get a json payload:
{"num_results": 1, "query": "postgresql", "results": [{"description": "", "name": "library/postgresql"}]}
to give more background here is how I started my registry:
docker run \
-e SETTINGS_FLAVOR=local \
-e STORAGE_PATH=/registry \
-e SEARCH_BACKEND=sqlalchemy \
-e LOGLEVEL=DEBUG \
-p 5000:5000 \
registry