# SVM derivation - using different classes

in every book I considered (like The Elements of Statictical Learning or An Introduction to Statistical Learning) the derivation of the SVM is always done with classes $$y_i \in \{-1,1 \}$$. In my problem, the classes are labeled as $$y_i \in \{0,1 \}$$. How can I adjust? Is it possible to do the derivation with $$y_i \in \{-1,1 \}$$ and then redefine the classes to $$\hat{y}_i \in \{0,1 \}$$?