By his own words, Obama has violated the Constitution with his action on Libya

Obama's own words from a December 2007 interview with the Boston Globe: "The President does not have power under the Constitution to unilaterally authorize a military attack in a situation that does not involve stopping an actual or imminent threat to the nation."

Did President Obama abide by the War Powers Act with his decision to fire Tomahawk missiles on Libya?

Nope.

Obama authorized the use of B-2 bombers and fighter aircraft to strike targets in major cities in Libya, to include the capital city of Tripoli.  That's an act of war.

Did President Obama insist that Congress officially declare war?

Nope.

So what has taken place?  The President has unilaterally authorized a military attack in a situation that does not involve stopping an actual or imminent threat to the nation.