On the convex hull of the union of certain polyhedra

Authors:
Egon Balas
Affiliations:
Management Science Research Group, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Venue:
Operations Research Letters
Year:
1988

Citing 0
Cited 2

Convexity recognition of the union of polyhedra

Computational Geometry: Theory and Applications
On the convex hull of feasible solutions to certain combinatorial problems

Operations Research Letters

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Abstract

We consider a finite collection of polyhedra whose defining linear systems differ only in their right hand sides. Jeroslow [5] and Blair [4] specified conditions under which the convex hull of the union of these polyhedra is defined by a system whose left hand side is the common lefthand side of the individual systems, and whose right hand side is a convex combination of the individual right hand sides. We give a new sufficient condition for this property to hold, which is often easier to recognize. In particular, we show that the condition is satisfied for polyhedra whose defining systems involve the node-arc incidence matrices of directed graphs, with certain righ hand sides. We also derive as a special case the compact linear characterization of the two terminal Steiner tree polytope given in Ball, Liu and Pulleyblank [3].