CVXPY
Minimize
  abs(x) + 1.0
Subject To
Bounds
 x free
End
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AFTER COMPILATION
Minimize
  C0
Subject To
 R0: - C0 + C1 <= 0
 R1: - C0 - C1 <= 0
Bounds
 C0 free
 C1 free
End
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GUROBI
Minimize
  0 x + abs_1 + Constant
Subject To
Bounds
 x free
 Constant = 1
General Constraints
 GC0: abs_1 = ABS ( x )
End