A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization

Xiyao Luo; Gang Ma; Xiaodong Hu; Yuqing Fu

doi:doi:10.11648/j.ajam.20160406.18

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A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization

Xiyao Luo, Gang Ma, Xiaodong Hu, Yuqing Fu

Published in American Journal of Applied Mathematics (Volume 4, Issue 6)

Received: 2 November 2016 Accepted: 6 December 2016 Published: 26 December 2016

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Abstract

In this paper, a class of large-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function are presented. The proposed kernel function is not only used for determining the search directions but also for measuring the distance between the given iterate and the center for the algorithms. By means of the Nesterov and Todd scaling scheme, the currently best known iteration bounds for large-update methods is established.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 6)
DOI	10.11648/j.ajam.20160406.18
Page(s)	316-323
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Interior-Point Methods, Semidefinite Optimization, Large-Update Methods, Polynomial Complexity

References

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[5]	El Ghami M., Bai Y. Q., Roos C.: Kernel-function based Algorithms for semidefinite optimization. RAIRO Oper. Res. 43(2), 189-199 (2009)
[6]	Lee Y. H., Cho Y. Y., Jin J. H., Cho G. M.: Interior-point algorithms for LO and SDO based on a new class of kernel functions. J. Nonlinear Convex Anal. 13(3), 555-573 (2012)
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[9]	Wang G. Q., Bai Y. Q.: Primal-dual interior-point algorithms for convex quadratic semidefinite optimization. Nonlinear Anal. 71(7-8), 3389-3402 (2009)
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[14]	Zhang M. W.: A large-update interior-point algorithm for convex quadratic semidefinite optimization based on a new kernel function. Acta Math. Sin. (Engl. Ser.) 28(11), 2313-2328 (2012)
[15]	Bai, Y. Q., El Ghami, M., Roos, C.: A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization. SIAM J. Optim. 15(1), 101-128 (2004)
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APA Style

Xiyao Luo, Gang Ma, Xiaodong Hu, Yuqing Fu. (2016). A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization. American Journal of Applied Mathematics, 4(6), 316-323. https://doi.org/10.11648/j.ajam.20160406.18

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ACS Style

Xiyao Luo; Gang Ma; Xiaodong Hu; Yuqing Fu. A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization. Am. J. Appl. Math. 2016, 4(6), 316-323. doi: 10.11648/j.ajam.20160406.18

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AMA Style

Xiyao Luo, Gang Ma, Xiaodong Hu, Yuqing Fu. A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization. Am J Appl Math. 2016;4(6):316-323. doi: 10.11648/j.ajam.20160406.18

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@article{10.11648/j.ajam.20160406.18,
  author = {Xiyao Luo and Gang Ma and Xiaodong Hu and Yuqing Fu},
  title = {A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {316-323},
  doi = {10.11648/j.ajam.20160406.18},
  url = {https://doi.org/10.11648/j.ajam.20160406.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.18},
  abstract = {In this paper, a class of large-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function are presented. The proposed kernel function is not only used for determining the search directions but also for measuring the distance between the given iterate and the center for the algorithms. By means of the Nesterov and Todd scaling scheme, the currently best known iteration bounds for large-update methods is established.},
 year = {2016}
}

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TY  - JOUR
T1  - A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization
AU  - Xiyao Luo
AU  - Gang Ma
AU  - Xiaodong Hu
AU  - Yuqing Fu
Y1  - 2016/12/26
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DO  - 10.11648/j.ajam.20160406.18
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
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PB  - Science Publishing Group
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AB  - In this paper, a class of large-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function are presented. The proposed kernel function is not only used for determining the search directions but also for measuring the distance between the given iterate and the center for the algorithms. By means of the Nesterov and Todd scaling scheme, the currently best known iteration bounds for large-update methods is established.
VL  - 4
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Author Information

Xiyao Luo

College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, China
Gang Ma

College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, China
Xiaodong Hu

College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, China
Yuqing Fu

College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, China

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APA Style

Xiyao Luo, Gang Ma, Xiaodong Hu, Yuqing Fu. (2016). A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization. American Journal of Applied Mathematics, 4(6), 316-323. https://doi.org/10.11648/j.ajam.20160406.18

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ACS Style

Xiyao Luo; Gang Ma; Xiaodong Hu; Yuqing Fu. A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization. Am. J. Appl. Math. 2016, 4(6), 316-323. doi: 10.11648/j.ajam.20160406.18

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AMA Style

Xiyao Luo, Gang Ma, Xiaodong Hu, Yuqing Fu. A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization. Am J Appl Math. 2016;4(6):316-323. doi: 10.11648/j.ajam.20160406.18

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@article{10.11648/j.ajam.20160406.18,
  author = {Xiyao Luo and Gang Ma and Xiaodong Hu and Yuqing Fu},
  title = {A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {316-323},
  doi = {10.11648/j.ajam.20160406.18},
  url = {https://doi.org/10.11648/j.ajam.20160406.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.18},
  abstract = {In this paper, a class of large-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function are presented. The proposed kernel function is not only used for determining the search directions but also for measuring the distance between the given iterate and the center for the algorithms. By means of the Nesterov and Todd scaling scheme, the currently best known iteration bounds for large-update methods is established.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization
AU  - Xiyao Luo
AU  - Gang Ma
AU  - Xiaodong Hu
AU  - Yuqing Fu
Y1  - 2016/12/26
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.18
DO  - 10.11648/j.ajam.20160406.18
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 316
EP  - 323
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.18
AB  - In this paper, a class of large-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function are presented. The proposed kernel function is not only used for determining the search directions but also for measuring the distance between the given iterate and the center for the algorithms. By means of the Nesterov and Todd scaling scheme, the currently best known iteration bounds for large-update methods is established.
VL  - 4
IS  - 6
ER  -

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