Looking for alternatives to F5 load balancer

Most of the stuff can be done by hand on commodity hardware using the Free and Open Source HAProxy which also natively supports TLS/SSL termination. With its impressive feature set, HAProxy is by now the standard loadbalancing solution for a wide range of applications.

There is commercial support available from the people developing HAProxy as well as external vendors like like Loadbalancer.org or Exceliance which package that all up into appliances with enterprise support and additional goodies.

But the biggest point here is that the price is MUCH lower than the big guys with equal or better performance.

How about Zeus's ZXTM? The entire content of the BBC goes through four of them, we have two - not cheap but seriously flexible/configurable plus a super fast cache too. Think it hits all/most of your requirements, take a look.