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

Published online by Cambridge University Press:  17 May 2008

M. EL Ghami  and
C. Roos
M. EL Ghami
Affiliation:
Department of Informatics, University of Bergen, Thormøblensgate 55, 5008 Bergen, Norway; [email protected]
C. Roos
Affiliation:
Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, PO Box 5031, 2600 GA Delft, The Netherlands; [email protected]
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Abstract

In this paper we present a generic primal-dualinterior 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.

Keywords

Linear optimizationprimal-dual interior-point algorithmlarge and small-update method.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 2: CIRO 05 , April 2008 , pp. 199 - 213
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

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