CVXPY
Minimize
  Sum(X + Y, None, False)
Subject To
 24: [ 2. -1.] <= minimum(X, Y)
Bounds
 X free
 Y free
End
----------------------------------------
AFTER COMPILATION
Minimize
  x_0 + x_1 + x_2 + x_3
Subject To
 R0: - x_0 - x_4 <= 0
 R1: - x_1 - x_5 <= 0
 R2: - x_2 - x_4 <= 0
 R3: - x_3 - x_5 <= 0
 R4: x_4 <= -2
 R5: x_5 <= 1
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
 x_5 free
End
----------------------------------------
GUROBI
Minimize
  X[0] + X[1] + Y[0] + Y[1]
Subject To
 24[0]: minimum_1 >= 2
 24[1]: minimum_2 >= -1
Bounds
 X[0] free
 X[1] free
 Y[0] free
 Y[1] free
 minimum_1 free
 minimum_2 free
General Constraints
 GC0: minimum_1 = MIN ( X[0] , Y[0] )
 GC1: minimum_2 = MIN ( X[1] , Y[1] )
End