A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms ∗ Y. Q. Bai 1 Jinli Guo 2 C. Roos 3 April 3, 2006 1 Department of Mathematics, Shanghai University, Shanghai, 200436, China 2 College of Management, University of Shanghai for Science and Technology Shanghai, 200093, China 3 Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands e-mail: yqbai@staff.shu.edu.cn, phd5816@163.com, c.roos@ewi.tudelft.nl Abstract Kernel functions play an important role in defining new search directions for primal-dual interior- point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields the best known complexity bound, both for large- and for small-update methods. The analysis in this paper uses the analysis scheme presented in [2]. Keywords: Linear optimization, interior-point method, primal-dual method, large-update method, polynomial complexity. AMS Subject Classification: 90C05, 90C51 1 Introduction We consider linear optimization (LO) problem in standard format: (P ) min{c T x : Ax = b,x ≥ 0}, where A ∈ IR m×n , rank(A)= m, b ∈ IR m ,c ∈ IR n , and its dual problem (D) max{b T y : A T y + s = c,s ≥ 0}. ∗ The first and the third author kindly acknowledge the support of the Dutch Organization for Scientific Research (NWO grant B61-569) 1