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 (Formula presented.) -representation and (Formula presented.) -representation. In this paper, we introduce the concept of a minimal (Formula presented.) -representation for semi-closed polyhedra which can be regarded as a natural extension of a minimal (Formula presented.) -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.
Original language | English |
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Pages (from-to) | 761-770 |
Number of pages | 10 |
Journal | Optimization |
Volume | 64 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- generators
- minimal representation
- refining criteria
- semi-closed polyhedra
ASJC Scopus subject areas
- Applied Mathematics
- Control and Optimization
- Management Science and Operations Research