Using Simplify[Minimize[{term2, b >= c > b/2 >= 0 && a >= d > a/2 >= 0}, {c,d}]] I was able to get the following output:
I am now wondering how to properly interprete the result. On the left hand side I can see that there are three possible minimized values of the expression. But then, $c$ and $d$ have only two results. Also since, there is the # sign in the $c$ value, what does it mean? Were we able to find a solution or not really? Sorry for asking super basic questions. It's just I couldn't find a nice explanation online.

#are just additional variables in theRootexpression - i.e $c$ is the root of that multinomial in variables $a, b, #_1$ – flinty Aug 07 '21 at 11:01Root. – Michael E2 Aug 07 '21 at 13:45Piecewiseexpression tells you explicitly the domain for each of its values. Note that when posting questions include all code and data (both in copy and paste-ableInputForm) needed to reproduce the results. Without the definition ofterm2we cannot produce results that we can read. – Bob Hanlon Aug 07 '21 at 14:52