Unbounded time verification of hybrid systems is a challenging  
problem. In this talk, we discuss how strategy improvement algorithms,  
as used for the analysis of two-players zero-sum games, can be applied  
for performing template-based unbounded time verification of hybrid  
systems using abstract interpretation. In order to do so, we in a  
first step recast the verification problem into a purely mathematical  
optimization problem. In a second step, we discuss two recently  
developed strategy improvement algorithms that can be used to tackle  
the obtained mathematical optimization problem. Finally, we discuss  
the consequences of using these approaches for performing template- 
based unbounded time verification of hybrid systems.