Explicit description of separating and supporting hyperplanes of two convex polyhedral sets depending on parameters

Abstract

We study separation of convex polyhedra under uncertainty. Uncertainty is treated both with the help of parametrization and interval analysis.

In the parametrization part of this work we study three main cases: parameters are situated either in the right-hand side of inequalities, or in one row or in one column of the constraint matrix. For each case we are concerned with the basic separation properties (existence, description, stability etc.) of two convex polyhedral sets with parameters.

We define so called solution set and stability sets. We provide a lot of examples, which were carried out on a computer.

Interval analysis deals with real intervals instead of real numbers. We propose a way how to check whether given convex polyhedral sets are separable for some or for all realizations of the interval data.