[SCIP] Questions regarding the gap with MINLP

[Pavlos Bekiaris]

Hello everyone :D 

I've got two questions about the gap that SCIP uses for MINLP (I hope the questions are not too silly, for which I'd like to pre-emptively apologize!). Coming from (mixed-integer) linear programming, a common definition of the gap is clear to me for (MI)LP as the current difference of the current best found optimum and the optimum of a relaxed problem. I also know that the gap in SCIP is defined in relation to the current difference of the primal and some dual optimization values (as detailed in your FAQ), but... 

1. For a non-convex MINLP, can I interpret the values of the primal and the dual value as boundaries of a region in which the ultimate optimal value lies? Or is it possible that both the dual and primal value shift further, so that the ultimate optimal value can lie somewhere out of any previous interval between primal and dual values? 
2. Also, I'd greatly appreciate any hint (maybe some publication or slides?) where some concepts about the dualization of a MINLP in SCIP are further explained. My searches in this direction failed, I'm probably just using the wrong terminology :3 

Kind regards :-) 
P.S.B. 
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