"The president has used military force without authorization from Congress." If that had simply happened, it would probably end up with an impeachment. The president cannot just do what he or she wants.
"Congress has authorized the use of military force without the support of the president." that is not the case. Specially when the question is about what the president does, not the congress.
"The president has used executive privilege to authorize the use of military force." executive privileges don't allow you to use military forces against other countries. That's a different kind of authority.
Which leaves us to the answer:
Congress has enacted joint resolutions to authorize the president to use military force
The President cannot use this power without the authorization of the congress, but since resolutions were passed in certain situations, like the " Authorization for Use of Military Force Against Iraq Resolution of 1991", the President was allowed to command the military forces without the need for the congress to declare war.
