CVXPY
Minimize
  x + y
Subject To
 18: 1.0 <= minimum(x, y, 3.0)
Bounds
 x free
 y free
End
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AFTER COMPILATION
Minimize
  C0 + C1
Subject To
 R0: - C0 - C2 <= 0
 R1: - C1 - C2 <= 0
 R2: - C2 <= 3
 R3: C2 <= -1
Bounds
 C0 free
 C1 free
 C2 free
End
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GUROBI
Minimize
  x[0] + y
Subject To
 18: minimum_1 >= 1
Bounds
 x[0] free
 y free
 minimum_1 free
General Constraints
 GC0: minimum_1 = MIN ( x[0] , y , 3 )
End