On the choice of parameters for power-series interior point algorithms in linear programming

In this paper the authors study higher-order interior point algorithms, especially power-series algorithms, for solving linear programming problems. Since higher-order differentials are not parameter-invariant, it is important to choose a suitable parameter for a power-series algorithm. They propose a parameter transformation to obtain a good choice of parameter, called a k-parameter, for general truncated power-series approximations. The authors give a method to find a k-parameter. This method is applied to two power-series interior point algorithms, which are built on a primal-dual algorithm and a dual algorithm, respectively. Computational results indicate that these higher-order power-series algorithms accelerate convergence compared to first-order algorithms by reducing the number of iterations. Also they demonstrate the efficiency of the k-parameter transformation to amend an unsuitable parameter in power-series algorithms.