In our recently published paper “A Computationally Useful Algebraic Representation of Nonlinear Disjunctive Convex Sets Using the Perspective Function” (write-up available here), we established a (not very restrictive) condition (in equation 4) that was needed for our algebraic representation to be 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 it in a visually intuitive way. The note is available below; alternatively, it can be downloaded here.