The increasing use of machine learning in practice and legal regulations like EU's GDPR cause the necessity to be able to explain the prediction and behavior of machine learning models. A prominent example of particularly intuitive explanations of AI models in the context of decision making are counterfactual explanations. Yet, it is still an open research problem how to efficiently compute counterfactual explanations for many models. We investigate how to efficiently compute counterfactual explanations for an important class of models, prototype-based classifiers such as learning vector quantization models. In particular, we derive specific convex and non-convex programs depending on the used metric.