CVXPY
Minimize
  Sum(X, None, False)
Subject To
 52: -1.0 <= minimum(X + [ 2. -1.], [ 2. -1.])
Bounds
 X free
End
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AFTER COMPILATION
Minimize
  C0 + C1
Subject To
 R0: - C0 - C2 <= 2
 R1: - C1 - C3 <= -1
 R2: - C2 <= 2
 R3: - C3 <= -1
 R4: C2 <= 1
 R5: C3 <= 1
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
End
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GUROBI
Minimize
  X[0] + X[1]
Subject To
 R0: - X[0] + index_1 = 2
 R1: - X[1] + index_3 = -1
 52[0]: minimum_2 >= -1
 52[1]: minimum_4 >= -1
Bounds
 X[0] free
 X[1] free
 index_1 free
 minimum_2 free
 index_3 free
 minimum_4 free
General Constraints
 GC0: minimum_2 = MIN ( index_1 , 2 )
 GC1: minimum_4 = MIN ( index_3 , -1 )
End