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: X. Z. Cai, G. Q. Wang, M. El Ghami, Y. J. Yue
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/710158
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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.
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institution OA Journals
issn 1085-3375
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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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