In our recently published paper “A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function” (available here), we establish the condition (in equation 4) under which our algebraic representation is equivalent to the original disjunctive program.

However, this condition is somewhat obscure. As such, the purpose of this expository note is to provide more insight around this condition in a visually intuitive way. The note can be downloaded here.