Polytopes and the simplex method
نویسنده
چکیده
ci = 1, and all Pi in Σ. For example, the line segment between two points P and Q is the convex hull of those two points. This is clearly convex. An extremal point of a convex region is a point that does not lie on the interior of a line segment in the region. Any convex region is the convex hull of its extremal points. As was proved in [Weyl:1935], the convex hull of any finite set of points and rays is a polytope—i.e. it can also be specified in terms of a finite set of affine inequalities.
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