New Interior-Point Algorithm for Symmetric Optimization Based on a Positive-Asymptotic Barrier Function

We define a new interior-point method (IPM), which is suitable for solving symmetric optimization (SO) problems. The proposed algorithm is based on a new search direction. In order to obtain this direction, we apply the method of algebraically equivalent transformation on the centering equation of the central path. We prove that the associated barrier cannot be derived from a usual kernel function. Therefore, we introduce a new notion, namely the concept of the positive-asymptotic kernel function. We conclude that this algorithm solves the problem in polynomial time and has the same complexity as the best known IPMs for SO.