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A new proximity function generating the best known iteration bounds for both large-update and small-update interior-point methods

Published online by Cambridge University Press:  17 February 2009

Keyvan Aminis  and
Arash Haseli
Keyvan Aminis
Affiliation:
department of Sciences Razi University, Kermanshah Iran; email: [email protected] or [email protected].
Arash Haseli
Affiliation:
Islamic Azad University Kermanshah branch, Kermanshah Iran; email: [email protected].
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Abstract

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Interior-Point Methods (IPMs) are not only very effective in practice for solving linear optimization problems but also have polynomial-time complexity. Despite the practical efficiency of large-update algorithms, from a theoretical point of view, these algorithms have a weaker iteration bound with respect to small-update algorithms. In fact, there is a significant gap between theory and practice for large-update algorithms. By introducing self-regular barrier functions, Peng, Roos and Terlaky improved this gap up to a factor of log n. However, checking these self-regular functions is not simple and proofs of theorems involving these functions are very complicated. Roos el al. by presenting a new class of barrier functions which are not necessarily self-regular, achieved very good results through some much simpler theorems. In this paper we introduce a new kernel function in this class which yields the best known complexity bound, both for large-update and small-update methods.

Keywords

linear optimizationinterior-point methodprimal-dual methodkernel functionlarge-updatesmall-updatepolynomial complexity.
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 2 , October 2007 , pp. 259 - 270
Copyright
Copyright © Australian Mathematical Society 2007

References

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