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 )?

Question

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    )?

barbesdestyle2k · Accepted Answer

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

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

Answered question

Answer & Explanation

New Questions in Algebra I