Generic Primal-dual Interior Point Methods Based on a New Kernel Function

M. EL Ghami; C. Roos

RAIRO - Operations Research (2008)

  • Volume: 42, Issue: 2, page 199-213
  • ISSN: 0399-0559

Abstract

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In this paper we present a generic primal-dual interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2]. We show that the corresponding large-update algorithm improves the iteration complexity with a factor n 1 6 when compared with the method based on the use of the classical logarithmic barrier function. For small-update interior point methods the iteration bound is O ( n log n ϵ ) , which is currently the best-known bound for primal-dual IPMs.

How to cite

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EL Ghami, M., and Roos, C.. "Generic Primal-dual Interior Point Methods Based on a New Kernel Function." RAIRO - Operations Research 42.2 (2008): 199-213. <http://eudml.org/doc/250421>.

@article{ELGhami2008,
abstract = { In this paper we present a generic primal-dual interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2]. We show that the corresponding large-update algorithm improves the iteration complexity with a factor $n^\{\frac16\}$ when compared with the method based on the use of the classical logarithmic barrier function. For small-update interior point methods the iteration bound is $O(\sqrt\{n\}\log\frac\{n\}\{\epsilon\}),$ which is currently the best-known bound for primal-dual IPMs. },
author = {EL Ghami, M., Roos, C.},
journal = {RAIRO - Operations Research},
keywords = {Linear optimization; primal-dual interior-point algorithm; large and small-update method.; linear optimization; large and small-update method},
language = {eng},
month = {5},
number = {2},
pages = {199-213},
publisher = {EDP Sciences},
title = {Generic Primal-dual Interior Point Methods Based on a New Kernel Function},
url = {http://eudml.org/doc/250421},
volume = {42},
year = {2008},
}

TY - JOUR
AU - EL Ghami, M.
AU - Roos, C.
TI - Generic Primal-dual Interior Point Methods Based on a New Kernel Function
JO - RAIRO - Operations Research
DA - 2008/5//
PB - EDP Sciences
VL - 42
IS - 2
SP - 199
EP - 213
AB - In this paper we present a generic primal-dual interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2]. We show that the corresponding large-update algorithm improves the iteration complexity with a factor $n^{\frac16}$ when compared with the method based on the use of the classical logarithmic barrier function. For small-update interior point methods the iteration bound is $O(\sqrt{n}\log\frac{n}{\epsilon}),$ which is currently the best-known bound for primal-dual IPMs.
LA - eng
KW - Linear optimization; primal-dual interior-point algorithm; large and small-update method.; linear optimization; large and small-update method
UR - http://eudml.org/doc/250421
ER -

References

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  3. Y.Q. Bai, M. El Ghami, and C. Roos, A new efficient large-update primal-dual interior-point method based on a finite barrier. SIAM J. Optim.13 (2003) 766-782.  Zbl1036.90051
  4. Y.Q. Bai, C. Roos, and M. El Ghami, A primal-dual interior-point method for linear optimization based on a new proximity function. Optim. Methods Softw.17 (2002) 985–1008.  Zbl1032.90068
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  12. J. Peng, C. Roos, and T. Terlaky, Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press, 2002.  Zbl1136.90045
  13. C. Roos, T. Terlaky, and J.-P. Vial, Theory and Algorithms for Linear Optimization. An Interior-Point Approach. John Wiley & Sons, Chichester, UK, 1997.  Zbl0954.65041
  14. G. Sonnevend, An “analytic center” for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming. In System Modelling and Optimization : Proceedings of the 12th IFIP- Conference held in Budapest, Hungary, September 1985, edited by A. Prékopa, J. Szelezsán, and B. Strazicky, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, West–Germany, 84 (1986) 866–876.  
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