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

¹ Department of Informatics, University of Bergen, Thormøblensgate 55, 5008 Bergen, Norway; melghami@ii.uib.no
² Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, PO Box 5031, 2600 GA Delft, The Netherlands; C.Roos@ewi.tudelft.nl

Received: 9 February 2007
Accepted: 28 November 2007

Abstract

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