In[40]:= FindMinimum[{x + y,
Element[{x, y},
ParametricRegion[{Cos[\[Theta]],
Sin[\[Theta]]}, {{\[Theta], 0, 2 \[Pi]}}]]}, {{x, -.7}, {y, -.7}}]
Out[40]= {1., {x -> 1., y -> 2.22537*10^-8}}
In[39]:= NMinimize[{x + y,
Element[{x, y},
ParametricRegion[{Cos[\[Theta]],
Sin[\[Theta]]}, {{\[Theta], 0, 2 \[Pi]}}]]}, {x, y}]
Out[39]= {-1.41421, {x -> -0.707107, y -> -0.707107}}
The FindMinimum result is wrong, even though the starting point is quite close to the actual minimum.
