Most, if not all, Christians would answer that question with an unqualified “Yes.” But in a recent couple of blog posts, well-known Arminian theologian Roger Olson says “No.” In his own words: “In a recent post I said Arminians should not pray for God to save their friends and loved ones.” While this may be shocking to most Christians, Olson is quite honest about the limitations of the Arminian God, who has no power over the libertarian free will of human beings. Thus asking God to save someone unconditionally is impossible, according to Olson. You can find his discussion here and here.
Of course, we can ask God, and God can unilaterally save someone, not because he forces people to accept the gospel against their free will, but because he alone is able to change the rebellious heart of the unbeliever so that he or she willingly, of their own will, repents and believes the gospel. Only God can save the lost—but he can do it, and he is not limited by the depravity of the human will.