A note on central cutting plane methods for convex programming

Most cutting plane methods, like that of Kelley and Cheney and Goldstein solve a linear approximation (localization) of the problem, and then generate an additional cut to remove the linear program's optimal point. Other methods, like the \central cutting" plane methods, calculate a center of the linear approximation and then adjust the level of the objective, or separate the current center from the feasible set. In this paper we present a uni ed treatment of Elzinga and Moore's and Go n and Vial's central cutting plane methods. It is shown that Go n and Vial's method enjoys the same convergence properties as Elzinga and Moore's method.