To ensure user satisfaction and success of mobile applications, it is important to provide highly performant applications. This is particularly important for resource-constrained systems such as mobile devices. Thereby, non-functional performance characteristics, such as energy and memory consumption, play an important role for user satisfaction. This paper provides a comprehensive survey of non-functional performance optimization for Android applications. We collected 156 unique publications, published between 2008 and 2020, that focus on the optimization of non-functional performance of mobile applications. We target our search at four performance characteristics: responsiveness, launch time, memory and energy consumption. For each performance characteristic, we categorize optimization approaches based on the method used in the corresponding publications. Furthermore, we identify research gaps in the literature for future work.