Computing bounding box of polytope (system of linear inequalities)Given a N real valued variables and a set of linear inequality constraints, I would like to find a minimal bounding box which encapsulates the convex polytope defined by these constraints.

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Hailee Henderson · Accepted Answer

Let   P  =  {  x  ∈        R    M    |  A  x  ≤  b  } be the polytope, for some   A  ∈        R          N      ×      M       and   b  ∈        R    N  . Then, the (tightest) bounding box is the hypercube   [      α    1    ,      β    1    ]  ×  [      α    2    ,      β    2    ]  ×  …  [      α    M    ,      β    M    ], given by      α    k    :=      min          x      ∈          P            x    k    ,   and       β    k    :=      max          x      ∈          P            x    k    =  −      min          x      ∈          P        −      x    k    .

Computing bounding box of polytope (system of linear inequalities) Given a

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