CVXPY
Minimize
  Sum(abs(X + Promote(1.0, (2, 2))), None, False)
Subject To
Bounds
 0.0 <= X
End
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AFTER COMPILATION
Minimize
  C0 + C1 + C2 + C3
Subject To
 R0: - C0 + C4 <= -1
 R1: - C1 + C5 <= -1
 R2: - C2 + C6 <= -1
 R3: - C3 + C7 <= -1
 R4: - C0 - C4 <= 1
 R5: - C1 - C5 <= 1
 R6: - C2 - C6 <= 1
 R7: - C3 - C7 <= 1
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
End
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GUROBI
Minimize
  abs_2 + abs_4 + abs_6 + abs_8
Subject To
 R0: - X[0,0] + index_1 = 1
 R1: - X[0,1] + index_3 = 1
 R2: - X[1,0] + index_5 = 1
 R3: - X[1,1] + index_7 = 1
Bounds
 index_1 free
 index_3 free
 index_5 free
 index_7 free
General Constraints
 GC0: abs_2 = ABS ( index_1 )
 GC1: abs_4 = ABS ( index_3 )
 GC2: abs_6 = ABS ( index_5 )
 GC3: abs_8 = ABS ( index_7 )
End