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My version of Mathematica (11.1) apparently cannot do NMinimize within RegionPlot. It did work before (!) my last software update.

Here is an example from user GioMott having the same (unanswered) problem:

RegionPlot[
 First@NMinimize[1 + a t + b t^2, t] > 0, {a, 0, 3}, {b, 0, 4}]

This produce a long list of error messages.

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I tried to separate NMinimize

j[a_?NumericQ, b_?NumericQ] := First@NMinimize[1 + a t+ b t^2 , t]

but

RegionPlot[j[a, b] >= 0, {a, 1, 3}, {b, 1, 4}]
(*Show::gtype: Success is not a type of graphics. ... *)  

gives several error messages.

As a workaround you might try

zw = Flatten[Table[{a, b, j[a, b]}, {a, 0, 3, .1},{b, 0, 4, .1}], 1]
(*message: NMinimize::ubnd: The problem is unbounded.*)

Show[Graphics[{Point[Select[zw, #[[3]] > 0 &][[All,{1, 2}]]]}],Axes -> True, AxesLabel -> {a, b}]

enter image description here

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