This link really provided some insights into the idea that binary search implications into the optimization problems by giving the main theorem. I am not really confident that I get the idea of the main theorem suggested there. Are there any easy explanations, for the ideas, expressed in that tutorial?
The main requirement for binary search to work is that the array has to be sorted. Basically, the "main theorem" generalizes that requirement as needed for the generalized binary search on functions instead of arrays. From the article: