In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search in the sense that they compute a next iterate on a straight line determined by a search direction which approximates the central path. The proposed arc-search interior-point algorithm uses an arc for the approximation. We discuss the convergence property of the proposed algorithm. We also conduct numerical experiments on the CUTEst benchmark problems and compare the performance of the proposed arc-search algorithm with that of an line-search algorithm. Numerical results indicate that the proposed arc-search algorithm reaches the optimal solution using less iterations than a line-search algorithm.
Research Report B-491, Department of Mathematical and Computing Science, Tokyo Institute of Technology, September 2019