One Approach to Constructing a Minimal Convex Hull

摘要

The minimal convex hull of a subset of finite-dimensional space is constructed in a discrete fashion: at each step, we construct a new set that includes the inherited set. The procedure for finding the chain of sets involves geometrically evident constructions. This chain becomes stationary; i.e., from some number onward, all the sets of the chain being constructed coincide with the minimal convex hull. Our approach uses the principal result (Caratheodory's theorem) underlying the conventional approach to constructing a minimal convex hull.