CVXPY
Minimize
  Sum(abs(X + Y), None, False)
Subject To
Bounds
 0.0 <= X
 0.0 <= Y
End
----------------------------------------
AFTER COMPILATION
Minimize
  C0 + C1
Subject To
 R0: - C0 + C2 + C4 <= 0
 R1: - C1 + C3 + C5 <= 0
 R2: - C0 - C2 - C4 <= 0
 R3: - C1 - C3 - C5 <= 0
Bounds
 C0 free
 C1 free
End
----------------------------------------
GUROBI
Minimize
  abs_2 + abs_4
Subject To
 R0: - X[0] - Y[0] + index_1 = 0
 R1: - X[1] - Y[1] + index_3 = 0
Bounds
 index_1 free
 index_3 free
General Constraints
 GC0: abs_2 = ABS ( index_1 )
 GC1: abs_4 = ABS ( index_3 )
End