# NMinimize extremely slow for simple, non-oscillatory function on an interval

The minimum of $$f(x) = -(x+1/2 \sqrt{1-x})$$ for $$x$$ between $$0$$ and $$1$$ occurs at $$x=15/16$$ with $$f(15/16)=-17/16$$. This is a function that Mathematica evaluates quickly, and I have plotted the function and its minimum values below:

Mathematica quickly evaluates

Minimize[{-x - 1/2 Sqrt[1 - x] , x > 0, x < 1}, x]

but is extremely slow in evaluating

NMinimize[{-x - 1/2 Sqrt[1 - x] , x > 0, x < 1}, x]

(In fact, Mathematica appears to hang when I try to evaluate the above.)

Why is this and how can I speed up the evaluation? Is it the way I specified the bounds? I have in mind somewhat more complicated examples but I’m hoping to understand this simple example first. I’m running 12.0 Student Edition on Windows 10.