There isn't a built-in flag yet, but you can use

pip list --outdated --format=freeze | grep -v '^\-e' | cut -d = -f 1  | xargs -n1 pip install -U

Note: there are infinite potential variations for this. I'm trying to keep this answer short and simple, but please do suggest variations in the comments!

In older version of pip, you can use this instead:

pip freeze --local | grep -v '^\-e' | cut -d = -f 1  | xargs -n1 pip install -U

The grep is to skip editable ("-e") package definitions, as suggested by @jawache. (Yes, you could replace grep+cut with sed or awk or perl or...).

The -n1 flag for xargs prevents stopping everything if updating one package fails (thanks @andsens).