A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization
In this paper, we generalize the classical primal–dual logarithmic barrier method for linear optimization to convex quadratic optimization over symmetric cone by using Euclidean Jordan algebras. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd scaling sche...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Elsevier Inc.
2013
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/34134 |
| _version_ | 1848754139979317248 |
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| author | Wang, G. Yu, C. Teo, Kok Lay |
| author_facet | Wang, G. Yu, C. Teo, Kok Lay |
| author_sort | Wang, G. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we generalize the classical primal–dual logarithmic barrier method for linear optimization to convex quadratic optimization over symmetric cone by using Euclidean Jordan algebras. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd scaling scheme, and only full Nesterov–Todd step is used at each iteration. We derive the iteration bound that matches the currently best known iteration bound for small-update methods, namely, O(√rlog4/ε. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm. |
| first_indexed | 2025-11-14T08:35:40Z |
| format | Journal Article |
| id | curtin-20.500.11937-34134 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:35:40Z |
| publishDate | 2013 |
| publisher | Elsevier Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-341342017-09-13T15:33:38Z A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization Wang, G. Yu, C. Teo, Kok Lay polynomial complexity convex quadratic optimization interior-point methods Euclidean Jordan algebras small-update method In this paper, we generalize the classical primal–dual logarithmic barrier method for linear optimization to convex quadratic optimization over symmetric cone by using Euclidean Jordan algebras. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd scaling scheme, and only full Nesterov–Todd step is used at each iteration. We derive the iteration bound that matches the currently best known iteration bound for small-update methods, namely, O(√rlog4/ε. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm. 2013 Journal Article http://hdl.handle.net/20.500.11937/34134 10.1016/j.amc.2013.06.064 Elsevier Inc. restricted |
| spellingShingle | polynomial complexity convex quadratic optimization interior-point methods Euclidean Jordan algebras small-update method Wang, G. Yu, C. Teo, Kok Lay A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization |
| title | A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization |
| title_full | A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization |
| title_fullStr | A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization |
| title_full_unstemmed | A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization |
| title_short | A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization |
| title_sort | new full nesterov-todd step feasible interior-point method for convex quadratic symmetric cone optimization |
| topic | polynomial complexity convex quadratic optimization interior-point methods Euclidean Jordan algebras small-update method |
| url | http://hdl.handle.net/20.500.11937/34134 |