Conical Combination
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The conical hull of a set S is a convex set. In fact, it is the intersection of all convex cones containing S plus the origin. If S is a compact set (in particular, when it is a finite set of points), then the condition "plus the origin" is unnecessary. If we discard the origin, we can divide all coefficients by their sum to see that a conical combination is a convex combination scaled by a positive factor. In the plane, the conical hull of a circle passing through the origin is the open half-plane defined by the tangent line to the circle at the origin. Therefore, the "conical combination" an...
The conical hull of a set S is a convex set. In fact, it is the intersection of all convex cones containing S plus the origin. If S is a compact set (in particular, when it is a finite set of points), then the condition "plus the origin" is unnecessary. If we discard the origin, we can divide all coefficients by their sum to see that a conical combination is a convex combination scaled by a positive factor. In the plane, the conical hull of a circle passing through the origin is the open half-plane defined by the tangent line to the circle at the origin. Therefore, the "conical combination" and "conical hull" are more accurately to be called the "convex conical combination" and "convex conical hull" respectively.
