A large-update primal-dual interior-point algorithm for second-order cone optimization based on a new proximity function

摘要

In this paper, we propose a large-update primal-dual interior-point algorithm for second-order cone optimization (SOCO) based on a class of kernel functions consisting of a trigonometric barrier term. The algorithm starts from a strictly feasible point and generates a sequence of points converging to an optimal solution of the problem. Using a simple analysis, we show that the algorithm has O(root N log N log N/is an element of) worst case iteration complexity for large-update primal-dual interior point methods which coincides with the so far best-known iteration bound for SOCO.