CVXPY
Minimize
  Sum(abs(X) + [[1.00 -2.00]
 [3.00 4.00]], None, False)
Subject To
Bounds
 0.0 <= X
End
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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_6 <= 0
 R3: - x_3 + x_7 <= 0
 R4: - x_0 - x_4 <= 0
 R5: - x_1 - x_5 <= 0
 R6: - x_2 - x_6 <= 0
 R7: - x_3 - x_7 <= 0
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 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
   + 6 Constant
Subject To
Bounds
 Constant = 1
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] )
End