CVXPY
Minimize
  Sum(abs(X) + abs(Y), None, False)
Subject To
Bounds
 0.0 <= X
 0.0 <= Y
End
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AFTER COMPILATION
Minimize
  x_0 + x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7
Subject To
 R0: - x_0 + x_8 <= 0
 R1: - x_1 + x_9 <= 0
 R2: - x_2 + x_10 <= 0
 R3: - x_3 + x_11 <= 0
 R4: - x_0 - x_8 <= 0
 R5: - x_1 - x_9 <= 0
 R6: - x_2 - x_10 <= 0
 R7: - x_3 - x_11 <= 0
 R8: - x_4 + x_12 <= 0
 R9: - x_5 + x_13 <= 0
 R10: - x_6 + x_14 <= 0
 R11: - x_7 + x_15 <= 0
 R12: - x_4 - x_12 <= 0
 R13: - x_5 - x_13 <= 0
 R14: - x_6 - x_14 <= 0
 R15: - x_7 - x_15 <= 0
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
 x_5 free
 x_6 free
 x_7 free
End
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GUROBI
Minimize
  0 X[0,0] + 0 X[0,1] + 0 X[1,0] + 0 X[1,1] + abs_1 + abs_2 + abs_3 + abs_4
   + 0 Y[0,0] + 0 Y[0,1] + 0 Y[1,0] + 0 Y[1,1] + abs_5 + abs_6 + abs_7
   + abs_8
Subject To
Bounds
General Constraints
 GC0: abs_1 = ABS ( X[0,0] )
 GC1: abs_2 = ABS ( X[0,1] )
 GC2: abs_3 = ABS ( X[1,0] )
 GC3: abs_4 = ABS ( X[1,1] )
 GC4: abs_5 = ABS ( Y[0,0] )
 GC5: abs_6 = ABS ( Y[0,1] )
 GC6: abs_7 = ABS ( Y[1,0] )
 GC7: abs_8 = ABS ( Y[1,1] )
End