I have a docker container running MySQL-5.5 with host data volume. I am upgrading my container to MySQL-5.6. I am starting a new container with the same host volume. MySQL was c
I believe you need to modify your dockerfile to run mysql-upgrade before starting mysql. Although you might need to repair it as well as described in the references you provided. You should only need to run it once, then you can remove it from dockerfile. (I assume database is actually stored on the host file system and mounted in the docker.)
You could start MySQL using the 5.5 image and run mysqldump against it
docker run --rm --link mysqld mysql:5.5 \
mysqldump -h mysqld --all-databases > /your/host/machine/
And then start a new container using the 5.6 image and initialize it using the SQL dump
docker run -v /data/your_dump.sql:/docker-entrypoint-initdb.d/dump.sql mysql:5.6