AN INTERIOR-POINT METHOD FOR SYMMETRIC OPTIMIZATION BASED ON A NEW WIDE NEIGHBORHOOD

摘要

In this paper, we present a theoretical framework of an interior-point method for solving linear optimization problems over symmetric cones. First, we define a new neighborhood of the central path and show that the defined neighborhood is wider than the neighborhoods that are available. Then, the convergence of the algorithm is investigated and, using an elegant analysis and Euclidean Jordan algebra as a tool is shown that the iteration complexity coincides with the best-known one obtained by any feasible interior-point method that uses the Nesterov-Todd direction. Finally, numerical results show that the proposed algorithm is efficient and promising.