Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term
We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for linear optimization based on th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/710158 |
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| _version_ | 1850172807358447616 |
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| author | X. Z. Cai G. Q. Wang M. El Ghami Y. J. Yue |
| author_facet | X. Z. Cai G. Q. Wang M. El Ghami Y. J. Yue |
| author_sort | X. Z. Cai |
| collection | DOAJ |
| description | We introduce a new parametric kernel function, which is a combination of the classic kernel
function and a trigonometric barrier term, and present various properties of this new kernel function. A
class of large- and small-update primal-dual interior-point methods for linear optimization based on this
parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive
the iteration bounds for large-update methods, O(n2/3log(n/ε)), and small-update methods, O(nlog(n/ε)). These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions. |
| format | Article |
| id | doaj-art-cc724280dc244ff7bd01a867a5fa4a5f |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cc724280dc244ff7bd01a867a5fa4a5f2025-08-20T02:19:58ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/710158710158Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier TermX. Z. Cai0G. Q. Wang1M. El Ghami2Y. J. Yue3College of Advanced Vocational Technology, Shanghai University of Engineering Science, Shanghai 200437, ChinaCollege of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, ChinaNesna University College, Mathematics Section, 8700 Nesna, NorwayCollege of Advanced Vocational Technology, Shanghai University of Engineering Science, Shanghai 200437, ChinaWe introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for linear optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods, O(n2/3log(n/ε)), and small-update methods, O(nlog(n/ε)). These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.http://dx.doi.org/10.1155/2014/710158 |
| spellingShingle | X. Z. Cai G. Q. Wang M. El Ghami Y. J. Yue Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term Abstract and Applied Analysis |
| title | Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term |
| title_full | Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term |
| title_fullStr | Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term |
| title_full_unstemmed | Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term |
| title_short | Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term |
| title_sort | complexity analysis of primal dual interior point methods for linear optimization based on a new parametric kernel function with a trigonometric barrier term |
| url | http://dx.doi.org/10.1155/2014/710158 |
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