Minimum recession-compatible subsets of closed convex sets
A subset B of a closed convex set A is recession-compatible with respect to A if A can be expressed as the Minkowski sum of B and the recession cone of A. We show that if A contains no line, then there exists a recession-compatible subset of A that is minimal with respect to set inclusion. The proof...
| Main Authors: | , |
|---|---|
| Format: | Journal Article |
| Published: |
Springer
2012
|
| Online Access: | http://hdl.handle.net/20.500.11937/19910 |
| _version_ | 1848750163404783616 |
|---|---|
| author | He, Y. Sun, Jie |
| author_facet | He, Y. Sun, Jie |
| author_sort | He, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A subset B of a closed convex set A is recession-compatible with respect to A if A can be expressed as the Minkowski sum of B and the recession cone of A. We show that if A contains no line, then there exists a recession-compatible subset of A that is minimal with respect to set inclusion. The proof only uses basic facts of convex analysis and does not depend on Zorn’s Lemma. An application of this result to the error bound theory in optimization is presented. |
| first_indexed | 2025-11-14T07:32:28Z |
| format | Journal Article |
| id | curtin-20.500.11937-19910 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:32:28Z |
| publishDate | 2012 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-199102019-02-19T05:35:00Z Minimum recession-compatible subsets of closed convex sets He, Y. Sun, Jie A subset B of a closed convex set A is recession-compatible with respect to A if A can be expressed as the Minkowski sum of B and the recession cone of A. We show that if A contains no line, then there exists a recession-compatible subset of A that is minimal with respect to set inclusion. The proof only uses basic facts of convex analysis and does not depend on Zorn’s Lemma. An application of this result to the error bound theory in optimization is presented. 2012 Journal Article http://hdl.handle.net/20.500.11937/19910 10.1007/s10898-011-9662-9 Springer fulltext |
| spellingShingle | He, Y. Sun, Jie Minimum recession-compatible subsets of closed convex sets |
| title | Minimum recession-compatible subsets of closed convex sets |
| title_full | Minimum recession-compatible subsets of closed convex sets |
| title_fullStr | Minimum recession-compatible subsets of closed convex sets |
| title_full_unstemmed | Minimum recession-compatible subsets of closed convex sets |
| title_short | Minimum recession-compatible subsets of closed convex sets |
| title_sort | minimum recession-compatible subsets of closed convex sets |
| url | http://hdl.handle.net/20.500.11937/19910 |