Extended Convex Hull

Sweep Line Algorithm for Convex Hull Revisited

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

L-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS

The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

Convex hull of two quadratic or a conic quadratic and a quadratic inequality

In this paper we consider an aggregation technique introduced by Yıldıran [45] to study the convex hull of regions defined by two quadratic inequalities or by a conic quadratic and a quadratic inequality. Yıldıran [45] shows how to characterize the convex hull of open sets defined by two strict quadratic inequalities using Linear Matrix Inequalities (LMI). We show how this aggregation technique...

Measuring Interval Efficiency in Convex Hull of Data Using DEA

Compact formulations as a union of polyhedra

We explore one method for finding the convex hull of certain mixed integer sets. The approach is to break up the original set into a small number of subsets, find a compact polyhedral description of the convex hull of each subset, and then take the convex hull of the union of these polyhedra. The resulting extended formulation is then compact, its projection is the convex hull of the original s...

Sum of Sets of Integer Points of Common-Normal Faces of Integer Polyhedra

We consider the Minkowski sum of subsets of integer lattice, each of which is a set of integer points of a face of an extended submodular [Kashiwabara–Takabatake, Discrete Appl. Math. 131 (2003) 433] integer polyhedron supported by a common positive vector. We show a sufficient condition for the sum to contain all the integer points of its convex hull and a sufficient condition for the sum to i...