Generic primal-dual interior point methods based on a new kernel function

Ghami, M. El; Roos, C.

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 $n^{\frac{1}{6}}$ 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 $O(\sqrt{n}log\frac{n}{ϵ}),$ which is currently the best-known bound for primal-dual IPMs.

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