CVXPY
Minimize
  Sum(X, None, False)
Subject To
 52: 1.0 <= min(X + [[1.00 -2.00]
 [3.00 4.00]], None, False)
Bounds
 X free
End
----------------------------------------
AFTER COMPILATION
Minimize
  C0 + C1 + C2 + C3
Subject To
 R0: - C0 - C4 <= 1
 R1: - C1 - C4 <= 3
 R2: - C2 - C4 <= -2
 R3: - C3 - C4 <= 4
 R4: C4 <= -1
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
End
----------------------------------------
GUROBI
Minimize
  X[0,0] + X[0,1] + X[1,0] + X[1,1]
Subject To
 R0: - X[0,0] + AddExpression_1[0,0] = 1
 R1: - X[0,1] + AddExpression_1[0,1] = -2
 R2: - X[1,0] + AddExpression_1[1,0] = 3
 R3: - X[1,1] + AddExpression_1[1,1] = 4
 52: min_2 >= 1
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
 min_2 free
General Constraints
 GC0: min_2 = MIN ( AddExpression_1[0,0] , AddExpression_1[0,1] ,
   AddExpression_1[1,0] , AddExpression_1[1,1] )
End