CVXPY
Minimize
  norm1(X + -[[2.00 1.00]
 [-2.00 -4.00]])
Subject To
Bounds
 X free
End
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AFTER COMPILATION
Minimize
  C0 + C1 + C2 + C3
Subject To
 R0: - C0 + C4 <= 2
 R1: - C1 + C5 <= -2
 R2: - C2 + C6 <= 1
 R3: - C3 + C7 <= -4
 R4: - C0 - C4 <= -2
 R5: - C1 - C5 <= 2
 R6: - C2 - C6 <= -1
 R7: - C3 - C7 <= 4
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
 C5 free
 C6 free
 C7 free
End
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GUROBI
Minimize
  norm1_2
Subject To
 R0: - X[0,0] + AddExpression_1[0,0] = -2
 R1: - X[0,1] + AddExpression_1[0,1] = -1
 R2: - X[1,0] + AddExpression_1[1,0] = 2
 R3: - X[1,1] + AddExpression_1[1,1] = 4
Bounds
 X[0,0] free
 X[0,1] free
 X[1,0] free
 X[1,1] free
 AddExpression_1[0,0] free
 AddExpression_1[0,1] free
 AddExpression_1[1,0] free
 AddExpression_1[1,1] free
General Constraints
 GC0: norm1_2 = NORM ( 1 ) ( AddExpression_1[0,0] , AddExpression_1[0,1] ,
   AddExpression_1[1,0] , AddExpression_1[1,1] )
End