AN ELIGIBLE KERNEL BASED PRIMAL-DUAL INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION

It is well known that each kernel function denes aprimal-dual interior-point method (IPM). Most of polynomial-timeinterior-point algorithms for linear optimization (LO) are based onthe logarithmic kernel function ([9]). In this paper we dene anew eligible kernel function and propose a new search directionand proximity function based on this function for LO problems. We show that the new algorithm has O((log p)52pn log n log nε ) andO(q32(log p)3pn log nε ) iteration complexity for large- and small-update methods, respectively. These are currently the best knowncomplexity results for such methods. KCI Citation Count: 0