An Arc-search Interior Point Method in the 𝒩 − ∞ Neighborhood for Symmetric Optimization

In this paper, we propose an arc-search infeasible interior point algorithm for symmetric optimization using the negative infinity neighborhood of the central path. The algorithm searches the optimizers along the ellipses that approximate the entire central path. The convergence of the algorithm is shown for the set of commutative scaling class, which includes some of the most interesting choice of scalings such as xs, sx and the Nesterov-Todd scalings.