A variant of method of centers for convex optimization is considered. Given an upper bound on the objective function, the algorithm searches for an "approximate analytic center" of the current "set of localization". If that point is not a solution, the objective constraint is translated all the way to this approximate analytic center. The algorithm then finds an interior point in the updated set of localization and from there moves to an approximate analytic center of this updated set. The complexity of the algorithm will be established.
Published December 2001 , 13 pages