Convex hull characterizations of lexicographic orderings
Given a p-dimensional nonnegative, integral vector $$\varvec{\alpha },$$α,this paper characterizes the convex hull of the set S of nonnegative, integral vectors $$\varvec{x}$$xthat is lexicographically less than or equal to $$\varvec{\alpha }.$$α.To obtain a finite number of elements in S, the vect...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
25 April 2016
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| In: |
Journal of global optimization
Year: 2016, Volume: 66, Issue: 2, Pages: 311-329 |
| ISSN: | 1573-2916 |
| DOI: | 10.1007/s10898-016-0435-3 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s10898-016-0435-3
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| Author Notes: | Warren Adams, Pietro Belotti, Ruobing Shen |
| Summary: | Given a p-dimensional nonnegative, integral vector $$\varvec{\alpha },$$α,this paper characterizes the convex hull of the set S of nonnegative, integral vectors $$\varvec{x}$$xthat is lexicographically less than or equal to $$\varvec{\alpha }.$$α.To obtain a finite number of elements in S, the vectors $$\varvec{x}$$xare restricted to be component-wise upper-bounded by an integral vector $$\varvec{u}.$$u.We show that a linear number of facets is sufficient to describe the convex hull. For the special case in which every entry of $$\varvec{u}$$utakes the same value $$(n-1)$$(n-1)for some integer |
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| Item Description: | Gesehen am 03.08.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1573-2916 |
| DOI: | 10.1007/s10898-016-0435-3 |