Is it permissible to complete one's education without the father's knowledge, so long as he objects to it?

You must obey your father in what he commands you, and it is not permissible for you to complete your studies without his permission. However, if you can convince him and intercede with someone whose opinion he respects, then do so, provided that the institute is free of Shariah prohibitions. If your father agrees, then there is no harm; otherwise, obeying him takes precedence.