Abstract
A semi-closed polyhedron is defined as the intersection of finitely many closed and/or open half-spaces, which can be regarded as an extension of a polyhedron. The same as a polyhedron, a semi-closed polyhedron admits both -representation and -representation. In this paper, we introduce the concept of a minimal -representation for semi-closed polyhedra which can be regarded as a natural extension of a minimal -representation for polyhedra. We derive some criteria for refining generators of a semi-closed polyhedron. These refining criteria can be applied to obtain a minimal generator for a semi-closed polyhedron.
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