ABS Function may not work

Gurobi outputs x=0 and y=-1 for the given straightforward model, contrary to the expected values of x=-1 and y=0. It appears that the ABS function might be malfunctioning. I seek clarification to determine if this discrepancy stems from ABS-related issues or a potential misunderstanding in my model formulation. Any insights or comments on this matter would be greatly appreciated.
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Minimize
2 x + y
Subject To
diff: - x + y + diff1 = 0
abs_condition: absx >= 1
Bounds
-1 <= x <= 3
-1 <= y <= 3
Generals
x y
General Constraints
abs_value: absx = ABS ( diff1 )
End
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# Objective value = -1
x 0
y -1
diff1 1
absx 1

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Silke Horn

Gurobi Staff

November 16, 2023 09:29

Hi,

The issue is the lower bound of diff1. By default, variables have a lower bound of 0. Your solution x=-1 and y=0 is infeasible since it would require diff1=-1. If allow negative values for for diff1, you get the solution you expect.

Silke

Koji Nakano

November 16, 2023 10:07

Thank you.
I understand.
I can achieve the expected result by adding '-Inf <= diff1 <= Inf'.

ABS Function may not work

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