HA!!! It's really the Arminians who can't get this together. If you really believe in the free-will of man, why would you even pray for God to change the hearts of unbelievers? God never will invoke His sovereignty over their free will, otherwise it wouldn't be free will. This has always puzzled me even before I understood the Reformed faith.
The truth is we pray that God WILL change the hearts of men. We are praying that God will change their very nature so that they will come to Him. But it's up to God to grant our prayers and we humbly submit to His divine knowledge to know what is best and perfect and just. We are not praying to override their "free will" because there is no such thing. We are praying for God to GIVE them a new heart. And if God in His mercy gives them a new heart and they come to know Christ, it is because their name was written before the foundation of the worlds but God allowed us to play a small part in it. It is no different then God giving Adam the garden to till while God knew Adam's needs and provided the growth.
God commands us to pray. God also knows what we need. The only way we know God's will is for us to pray and to see whether it is granted or not. Whatever the answer we win because we understand God's will. That is why all our prayers find their "yes" in Him.
For the Calvinist however, prayer is a meaningless ritual since they hold that God has decided everything and hasn't considered prayer occurring in time.