The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers
The subject of this report concerns differential-geometric properties of the Nesterov-Todd search direction for linear optimization over symmetric cones. In particular, we investigate the rescaled asymptotics of the associated flow near the central path. Our results imply that the Nesterov-Todd dire...
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| Format: | Report |
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Unspecified
2003
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| _version_ | 1797067493940920320 |
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| author | Hauser, R |
| author_facet | Hauser, R |
| author_sort | Hauser, R |
| collection | OXFORD |
| description | The subject of this report concerns differential-geometric properties of the Nesterov-Todd search direction for linear optimization over symmetric cones. In particular, we investigate the rescaled asymptotics of the associated flow near the central path. Our results imply that the Nesterov-Todd direction arises as the solution of a Newton system defined in terms of a certain transformation of the primal-dual feasible domain. This transformation has especially appealing properties which generalize the notion of weighted analytic centers for linear programming. |
| first_indexed | 2024-03-06T21:57:05Z |
| format | Report |
| id | oxford-uuid:4d47ddf7-30fd-492b-a101-ba6fff008c56 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:57:05Z |
| publishDate | 2003 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:4d47ddf7-30fd-492b-a101-ba6fff008c562022-03-26T15:54:41ZThe Nesterov-Todd Direction and its Relation to Weighted Analytic CentersReporthttp://purl.org/coar/resource_type/c_93fcuuid:4d47ddf7-30fd-492b-a101-ba6fff008c56Mathematical Institute - ePrintsUnspecified2003Hauser, RThe subject of this report concerns differential-geometric properties of the Nesterov-Todd search direction for linear optimization over symmetric cones. In particular, we investigate the rescaled asymptotics of the associated flow near the central path. Our results imply that the Nesterov-Todd direction arises as the solution of a Newton system defined in terms of a certain transformation of the primal-dual feasible domain. This transformation has especially appealing properties which generalize the notion of weighted analytic centers for linear programming. |
| spellingShingle | Hauser, R The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers |
| title | The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers |
| title_full | The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers |
| title_fullStr | The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers |
| title_full_unstemmed | The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers |
| title_short | The Nesterov-Todd Direction and its Relation to Weighted Analytic Centers |
| title_sort | nesterov todd direction and its relation to weighted analytic centers |
| work_keys_str_mv | AT hauserr thenesterovtodddirectionanditsrelationtoweightedanalyticcenters AT hauserr nesterovtodddirectionanditsrelationtoweightedanalyticcenters |