The closed convex hull of certain extreme points

Area and Perimeter of the Convex Hull of Stochastic Points

Given a set P of n points in the plane, we study the computation of the probability distribution function of both the area and perimeter of the convex hull of a random subset S of P . The random subset S is formed by drawing each point p of P independently with a given rational probability πp. For both measures of the convex hull, we show that it is #P-hard to compute the probability that the m...

Disjunctive Programming: Properties of the Convex Hull of Feasible Points

In this paper we characterize the convex hull of feasible points for a disjunctive program, a class of problems which subsumes pure and mixed integer programs and many other nonconvex programming problems. Two representations are given for the convex hull of feasible points. each of which provides linear programming equivalents of the disjunctive program. The first one involves a number of new ...

On the convex hull of random points in a polytope

'This research was sponsored by the National Science Foundation under Grant No. ECS-8418392. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation or the US Government. On the Convex Hull of Random Points in a Polytope R e x A . D w y e r * ...

On the Most Likely Convex Hull of Uncertain Points

Consider a set of d-dimensional points where the existence or the location of each point is determined by a probability distribution. The convex hull of this set is a random variable distributed over exponentially many choices. We are interested in finding the most likely convex hull, namely, the one with the maximum probability of occurrence. We investigate this problem under two natural model...

Extreme Points of Polar Convex Sets