Love is the answer.
When all hope is lost and you've lost your way, love one another. If I'm not mistaken I heard that from a song somewhere.
When we see acts of violence, we cannot use violence to correct it because it will only escalate further. Understanding that the perpetrator is merely acting in the way that he or she knows best to do, we will be able to project compassion. There is a possibility that in their childhood, they were in the receiving end of physical or sexual abuse, as how some psychologists explain it. This may be why the abusers turn out the way they do.
Using our a rational approach to them from the mindset of compassion, we should reach out and extend love to these "aggressors" and hopefully our actions will convince them that they are loved.
Once the everyone in the world is convinced of how loved they are, there will be no more room for insecurity or feeling of loss of control and need for violence. There will only be an urge to give back what has been given to them: love.