A full-Newton step interior-point algorithm based on modified-Newton direction

摘要

By a modification of the classic-Newton direction in scaled version for linear optimization, we give a new interior-point algorithm based on a very simple function. The algorithm uses full modified-Newton step, thus no need to perform line search. In the processing of the algorithm, the simple function is used to control the searching direction and measure the proximity of iterates to the central path. Moreover, the modified-Newton step used in the algorithm has local quadratic convergence property according to the proximity function. The iteration complexity is derived, and which is the best-known.