CVXPY
Minimize
  Sum(X, None, False)
Subject To
 39: -Y <= minimum(X, [ 2. -1.])
 44: Y == 1.0
Bounds
 X free
 Y free
End
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AFTER COMPILATION
Minimize
  C0 + C1
Subject To
 R0: C4 = 1
 R1: C5 = 1
 R2: - C0 - C2 <= 0
 R3: - C1 - C3 <= 0
 R4: - C2 <= 2
 R5: - C3 <= -1
 R6: C2 - C4 <= 0
 R7: C3 - C5 <= 0
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
 C5 free
End
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GUROBI
Minimize
  X[0] + X[1]
Subject To
 39[0]: - Y[0] - minimum_1 <= 0
 39[1]: - Y[1] - minimum_2 <= 0
 44[0]: Y[0] = 1
 44[1]: Y[1] = 1
Bounds
 X[0] free
 X[1] free
 Y[0] free
 Y[1] free
 minimum_1 free
 minimum_2 free
General Constraints
 GC0: minimum_1 = MIN ( X[0] , 2 )
 GC1: minimum_2 = MIN ( X[1] , -1 )
End