# NMinimize reports no points satisfy constraints

Set

f[a_?NumberQ, b_?NumberQ] := 5


and attempt

NMinimize[{f[a, b], a>0.1 && a<0.2 && b>0 && b<10 && Element[b,Integers], {a,b}]


The response is

NMinimize::nsol: There are no points that satisfy the constraints {}.


Yet if you try

NMinimize[{f[a, b], a>0.0 && a<0.2 && b>0 && b<10 && Element[b,Integers], {a,b}]


you get

{5., {a -> 0, b -> 6}}


Function is smooth with all derivatives.

{5., {a -> 0.15, b -> 6}}


would seem like a reasonable solution to the first request in light of the second.

I think this is worth reporting to Wolfram support. You can workaround the issue by using Mod:
NMinimize[

• this doesn't satisfy Element[b,Integers] though. – george2079 Dec 20 '17 at 22:23