System of Linear Inequalities to create feasible solution y = <mo movablelimits="true" for

groupweird40 2022-05-21 Answered
System of Linear Inequalities to create feasible solution y = min ( x 1 , x 2 )
The question is L 1 x 1 U 1 ,..., L n x n U n . Can we introduce decision variables and define a system of mixed-integer linear inequalities whose feasible solution is y = min ( x 1 , . . . , x n )?
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Answers (1)

barbesdestyle2k
Answered 2022-05-22 Author has 10 answers
I assume that there are other constraints on the x variables that are not listed; otherwise, just add the constraints x i = L i and y = min i L i . With that assumption in place, you could add binary variables z 1 , , z n , along with constraints y i x i i, y i x i U i ( 1 z i ) i and i z i = 1
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