MATH 305 Lecture Notes - Lecture 2: Convex Combination, Polyhedron, Hyperplane
4 Apr 2016
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Definition: polyhedron polytope if it is bounded and nonempty. ) boundary points. A polyhedron is the intersection of a finite number of half-spaces and/or hyper-plane. (it is called. Points that lie in the polyhedron and on one or more of the half-spaces or hyper-planes are called. Points that lies in the polyhedron but not boundary points are called interior points. Let p1, p2, , pm be points in rn. A convex combination of p1, p2, , pm is any point p that can be written such that: p = a1p1 + a2p2 + . Where a1, a2, , am are non-negative numbers such that: a1 + a2 + . Example 1: identify some interior point, boundary point and corner points. Theorem 2. 3. 3: suppose that k is a bounded polyhedron with corner points k1, k2, , km. Then any point p in k is a convex combination of k1, k2, , km.
