2 research outputs found
Minimal Representations of a Face of a Convex Polyhedron and Some Applications
In this paper, we propose a method for determining all minimal representations of a face of
a polyhedron defined by a system of linear inequalities. Main difficulties for determining
prime and minimal representations of a face are that the deletion of one redundant constraint
can change the redundancy of other constraints and the number of descriptor index pairs for
the face can be huge. To reduce computational efforts in finding all minimal representations
of a face, we prove and use properties that deleting strongly redundant constraints does
not change the redundancy of other constraints and all minimal representations of a face
can be found only in the set of all prime representations of the face corresponding to the
maximal descriptor index set for it. The proposed method is based on a top-down search
strategy, is easy to implement, and has many computational advantages. Based on minimal
representations of a face, a reduction of degeneracy degrees of the face and ideas to improve
some known methods for finding all maximal efficient faces in multiple objective linear
programming are presented. Numerical examples are given to illustrate the method