Generic primal-dual interior point methods based on a new kernel function
RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 2, pp. 199-213.

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(nlogn ϵ), which is currently the best-known bound for primal-dual IPMs.

DOI : 10.1051/ro:2008009
Classification : 90C05, 90C31
Mots clés : linear optimization, primal-dual interior-point algorithm, large and small-update method
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Ghami, M. El; Roos, C. Generic primal-dual interior point methods based on a new kernel function. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 2, pp. 199-213. doi : 10.1051/ro:2008009. http://www.numdam.org/articles/10.1051/ro:2008009/

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