CVXPY
Minimize
  abs(X) + 1.0
Subject To
Bounds
 X free
End
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AFTER COMPILATION
Minimize
  x_0
Subject To
 R0: - x_0 + x_1 <= 0
 R1: - x_0 - x_1 <= 0
Bounds
 x_0 free
 x_1 free
End
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GUROBI
Minimize
  0 X[0] + abs_1 + Constant
Subject To
Bounds
 X[0] free
 Constant = 1
General Constraints
 GC0: abs_1 = ABS ( X[0] )
End