I honestly don't think they'll do anything too significant. They'll probably just have a more than usual police and security presence around the Olympic vicinity. I wouldn't be surprised if they get a little help from the National Guard as security. I don't know why the homeless are the only topic of discussion, as LA also has many gangs and with territory within the vicinity who might see the opportunity to assault, rob, or extort Olympic athletes who may travel on foot or whatnot for leisure activities.
Homeless people have rights; you can't just forcibly pick them up off the street and bus them to some mysterious location to never be seen again until after the Olympics; it would be too transparent and make California officials look bad.
The only thing they can do is encourage the homeless to seek shelter and hope that they decide to go/stay. They have 4 years to wisely use this time to get it together to help the homeless off the streets, and maybe,e depending on how they choose to do so, it may lead to California being applauded.