ON THE CHOICE OF PARAMETERS FOR POWER-SERIES INTERIOR-POINT ALGORITHMS IN LINEAR-PROGRAMMING

In this paper we study higher-order interior point algorithms, especia lly power-series algorithms, for solving Linear programming problems. Since higher-order differentials are not parameter-invariant, it is im portant to choose a suitable parameter for a power-series algorithm. W e propose a parameter transformation to obtain a good choice of parame ter, called a k-parameter, for general truncated power-series approxim ations. We give a method to find a k-parameter. This method is applied to two power-series interior point algorithms, which are built on a p rimal-dual algorithm and a dual algorithm, respectively. Computational results indicate that these higher-order power-series algorithms acce lerate convergence compared to first-order algorithms by reducing the number of iterations. Also they demonstrate the efficiency of the k-pa rameter transformation to amend an unsuitable parameter in power-serie s algorithms.