Want to solve poverty? Maybe it's time to try taxing it.
Tax poor people more than rich people. The government does it with everything it tries to reduce. Want people to smoke less - stick a tax on it. Want people to reduce their soda consumption - stick a tax on it. Want people to reduce fossil fuel consumption - stick a tax on it.
So why not with poverty? Tax the poor more than the rich. Give them an incentive to get off their ass and figure out how to add value to the world.
Would have the added effect of filtering immigrants who come here for the freedom and superior culture from the immigrants who come for the welfare benefits.