A PRIMAL-DUAL INTERIOR-POINT ALGORITHM BASED ON A NEW KERNEL FUNCTION

We propose a new primal-dual interior-point algorithm based on a new kernel function for linear optimization problems. New search directions and proximity functions are proposed based on the kernel function. We show that the new algorithm has O.pn log n log.n=// and O.pn log.n=// iteration bounds for large-update and small-update methods, respectively, which are currently the best known bounds for such methods.