The convex hull of a Banach–Saks set

Convex Hull, Set of Convex Combinations and Convex Cone

Let V be a real linear space. The functor ConvexComb(V ) yielding a set is defined by: (Def. 1) For every set L holds L ∈ ConvexComb(V ) iff L is a convex combination of V . Let V be a real linear space and let M be a non empty subset of V . The functor ConvexComb(M) yielding a set is defined as follows: (Def. 2) For every set L holds L ∈ ConvexComb(M) iff L is a convex combination of M . We no...

Computing the convex hull of a planar point set

In Figure 1, the set S consists of thirteen points. The output of a convex hull algorithm should be the list (p1, p2, p3, p4, p5, p6). We remark that the list storing the vertices of CH (S) can start with an arbitrary vertex. In the example, the list (p3, p4, p5, p6, p1, p2) would also be a valid output. ∗School of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6. E-mail: ...

Minimization of convex functions on the convex hull of a point set

A basic algorithm for the minimization of a differentiable convex function (in particular, a strictly convex quadratic function) defined on the convex hull of m points in R is outlined. Each iteration of the algorithm is implemented in barycentric coordinates, the number of which is equal tom. The method is based on a new procedure for finding the projection of the gradient of the objective fun...

Adaptive Planar Convex Hull Algorithm for a Set of Convex Hulls

The Convex Hull of a Sample

1. The convex hull of a random sample may be considered as one possible analogue of the range of a one-dimensional sample. Recent work along this line has dealt with the expected number of vertices, faces, surface area and other quantities connected with the convex hull of n independently and identically distributed random points in the plane and in higher dimensions. See Renyi and Salanke [6] ...