CVXPY
Minimize
  Pnorm(X + -[[2.00 1.00]
 [-2.00 -4.00]], 2)
Subject To
Bounds
 X free
End
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AFTER COMPILATION
Minimize
  x_0
Subject To
 R0: - x_0 + soc_t_0 = 0
 R1: - x_1 + soc_x_1 = -2
 R2: - x_2 + soc_x_2 = 2
 R3: - x_3 + soc_x_3 = -1
 R4: - x_4 + soc_x_4 = 4
 qc0: [ - soc_t_0 ^2 + soc_x_1 ^2 + soc_x_2 ^2 + soc_x_3 ^2 + soc_x_4 ^2 ]
   <= 0
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
 soc_x_1 free
 soc_x_2 free
 soc_x_3 free
 soc_x_4 free
End
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GUROBI
Minimize
  norm2_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: norm2_2 = NORM ( 2 ) ( AddExpression_1[0,0] , AddExpression_1[0,1] ,
   AddExpression_1[1,0] , AddExpression_1[1,1] )
End