CVXPY
Minimize
  Sum(X, None, False)
Subject To
 63: -2.0 <= minimum(X + [[1.00 -2.00]
 [3.00 4.00]], [[1.00 -2.00]
 [3.00 4.00]])
Bounds
 X free
End
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AFTER COMPILATION
Minimize
  C0 + C1 + C2 + C3
Subject To
 R0: - C0 - C4 <= 1
 R1: - C1 - C5 <= 3
 R2: - C2 - C6 <= -2
 R3: - C3 - C7 <= 4
 R4: - C4 <= 1
 R5: - C5 <= 3
 R6: - C6 <= -2
 R7: - C7 <= 4
 R8: C4 <= 2
 R9: C5 <= 2
 R10: C6 <= 2
 R11: C7 <= 2
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
 C5 free
 C6 free
 C7 free
End
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GUROBI
Minimize
  X[0,0] + X[0,1] + X[1,0] + X[1,1]
Subject To
 R0: - X[0,0] + index_1 = 1
 R1: - X[0,1] + index_3 = -2
 R2: - X[1,0] + index_5 = 3
 R3: - X[1,1] + index_7 = 4
 63[0,0]: minimum_2 >= -2
 63[0,1]: minimum_4 >= -2
 63[1,0]: minimum_6 >= -2
 63[1,1]: minimum_8 >= -2
Bounds
 X[0,0] free
 X[0,1] free
 X[1,0] free
 X[1,1] free
 index_1 free
 minimum_2 free
 index_3 free
 minimum_4 free
 index_5 free
 minimum_6 free
 index_7 free
 minimum_8 free
General Constraints
 GC0: minimum_2 = MIN ( index_1 , 1 )
 GC1: minimum_4 = MIN ( index_3 , -2 )
 GC2: minimum_6 = MIN ( index_5 , 3 )
 GC3: minimum_8 = MIN ( index_7 , 4 )
End