Proxy Mobile Internet Protocol have two versions P-MIPv4 and P-MIPv6.
It is integrated in to P-GW to assign the IP address when the user is moving. Lets say if you have assigned an IP address to you and you are moving from one place to another. In this case you would definately change your routers or gateways too so it doesn't mean that new router will assign you the new IP address for routing purpose.
A new router will configure the Proxy IP for you and will assume that you have same IP address that you have assigned. Your IP would be same but in his database it will be merged with other IP address.
So your mobility will be resumed, session will be same. That's how in LTE mobility can be achieved in LTE or Wimax.
There are also some concepts like Home agent who was the first agent for a user and then a Proxy agent who will assign the proxy address. Kind of.
Usually now in core network we are using GTP-c for the same purpose. You know tunnels and all. But in Wi-max. as you know LTE main purpose is convergence. So there GTP is not there. If a user is latched on non-3gpp elements then it can be useful.
That is what up to my knowledge. Please make it correct if i am wrong.