At this point, the description of your problem is too vague. Can you show us the complete detailed mathematics of your proleml, making clear what are input data and what are optimization (a.k.a. decision) variables? And show us your complete code, including for the partially specified optimization.
But first:
Have you tried to implement the examples in the link, and then tried to modify them to ensure your understanding of how partially specified optimization works?
Or: Do you really have a bilevel optimization problem? If so, look at Bi-level programming in CVX .