'To authorize' is a long-established verb in English. It means 'to give authority to', or, more simply, 'to allow'. It is sometimes spelled, in British English, authorise. For an explanation - and the reason why AWE prefers 'authorize' - go to -ise - -ize.
There is a new way of using it to mean 'to write', which to AWE's taste is completely unnecessary - and ugly. It is to be seen in texts of Computer Science (or at least popular Computer manuals) and elsewhere, where authorised seems to have been used to mean 'written', by derivation, one may suppose, from the noun author. (See verb "to author").
authorize' meaning 'to write' is completely unacceptable. It is acceptable in its original sense - where it is of value.
You may also like to look at Authoritarian - authoritative.