Abstract

One of the central questions of polyhedral combinatorics is the question of the algorithmic relationship between vertex and facet descriptions of convex polytopes. In the sense of combinatorial optimization the reason for the relevance of this issue is the possibility of application of convex analysis methods to the decision combinatorial problems [6, 10, 15]. In this paper we consider combinatorial polytopes sufficiently general form. A number of necessary conditions and sufficient conditions for support inequality of polytope to be facet inequality are obtained, an illustration of the use of the developed technology to the connected k-factors polytope are given. Also we discuss the use of facet inequalities in cutting plane algorithms.

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