CVXPY
Minimize
  x + y
Subject To
 12: 1.0 <= minimum(x, y)
Bounds
 x free
 y free
End
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AFTER COMPILATION
Minimize
  x_0 + x_1
Subject To
 R0: - x_0 - x_2 <= 0
 R1: - x_1 - x_2 <= 0
 R2: x_2 <= -1
Bounds
 x_0 free
 x_1 free
 x_2 free
End
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GUROBI
Minimize
  x[0] + y
Subject To
 12: minimum_1 >= 1
Bounds
 x[0] free
 y free
 minimum_1 free
General Constraints
 GC0: minimum_1 = MIN ( x[0] , y )
End