NMinimize reports no points satisfy constraints

Question

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.

Answer 1

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

NMinimize[
    f[a, b],
    a>0.1 && a<0.2 && b>0 && b<10 && Mod[b,1]==0,
    {a, b}
]

{5., {a -> 0.145338, b -> 9.82944*10^-9}}