Minimize can only do this problem if the constraint is Reduced first

GROUPS:
 Frank Kampas 1 Vote Consider the following code: In[1]:= Minimize[{x^2 - y^2, Cos[x - y] >= 1/2, -5 <= x <= 5, -5 <= y <= 5}, {x, y}] Out[1]= Minimize[{x^2 - y^2, Cos[x - y] >= 1/2, -5 <= x <= 5, -5 <= y <= 5}, {x, y}] In[3]:= r = Reduce[{Cos[x - y] >= 1/2, -5 <= x <= 5, -5 <= y <= 5}, {x, y}] Out[3]= (-5 <= x < 1/3 (15 - 7 \[Pi]) && 1/3 (5 \[Pi] + 3 x) <= y <= 1/3 (7 \[Pi] + 3 x)) || (1/3 (15 - 7 \[Pi]) <= x < 1/3 (15 - 5 \[Pi]) && 1/3 (5 \[Pi] + 3 x) <= y <= 5) || (x == 1/3 (15 - 5 \[Pi]) && y == 5) || (-5 <= x <= 1/3 (-15 + \[Pi]) && -5 <= y <= 1/3 (\[Pi] + 3 x)) || (1/3 (-15 + \[Pi]) < x < (15 - \[Pi])/3 && 1/3 (-\[Pi] + 3 x) <= y <= 1/3 (\[Pi] + 3 x)) || ((15 - \[Pi])/3 <= x <= 5 && 1/3 (-\[Pi] + 3 x) <= y <= 5) || (x == 1/3 (-15 + 5 \[Pi]) && y == -5) || (1/3 (-15 + 5 \[Pi]) < x <= 1/3 (-15 + 7 \[Pi]) && -5 <= y <= 1/3 (-5 \[Pi] + 3 x)) || (1/3 (-15 + 7 \[Pi]) < x <= 5 && 1/3 (-7 \[Pi] + 3 x) <= y <= 1/3 (-5 \[Pi] + 3 x)) In[4]:= Minimize[{x^2 - y^2, r}, {x, y}] Out[4]= {1/9 (-150 \[Pi] + 25 \[Pi]^2), {x -> 5 - (5 \[Pi])/3, y -> 5}}