Method for minimization of quasiconvex functions based on logarithmic barriers

An iterative method for minimizing quasiconvex Lipschitz functions defined on convex compacts is described. The method is based on the cutting scheme with the cutting center being the analytic center of an auxiliary polyhedron containing the desired minimizer. The convergence rate of the method is established. A modification of the method for several special classes of quasiconvex functions is given.