An Arc Search Infeasible Interior-Point Algorithm for Symmetric Optimization Using a New Wide Neighborhood

In this paper, we propose an infeasible interior-point algorithm for symmetric optimization problems using a new wide neighborhood and estimating the central path by an ellipse. In contrast of most interior-point algorithms for symmetric optimization which search an e-optimal solution of the problem in a small neighborhood of the central path, our algorithm searches for optimizers in a new wide neighborhood of the ellipsoidal approximation of central path. The convergence analysis of the algorithm is shown and it is proved that the iteration bound of the algorithm is O(r log epsilon(-1)) which improves the complexity bound of the recent proposed algorithm by Liu et al. (J. Optim. Theory Appl., 2013, https://doi. org/10.1007/s10957-013-0303-y) for symmetric optimization by the factor r 12 and matches the currently best-known iteration bound for infeasible interior-point methods.