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

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