Cutting plane methods based on the analytic barrier for minimization of a convex function subject to box-constraints

We analyze three variants of analytic barrier methods for minimization of a convex function under box-constraints: the classical method of analytic barriers (centres), the proximal method of analytic barriers and the modified proximal method of analytic barriers. We give theoretical and practical complexity estimates of these methods and based on numerical tests outline their dependence on the used control parameters. We consider also the case where the objective function is not given in explicit analytic form and may not be defined everywhere.