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

infogus88

infogus88

Answered question

2022-05-19

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.

Answer & Explanation

Hailee Henderson

Hailee Henderson

Beginner2022-05-20Added 12 answers

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 .

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