Note on Central Cutting Plane Methods for Convex Programming

摘要

Most cutting plane methods, like that of Kelley and Cheney and Goldstein solve alinear 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 the paper the authors present a unified treatment of Elzinga and Moore's and Goffin and Vial's central cutting plane methods. It is shown that Goffin and Vial's method enjoys the same convergence properties as Elzinga and Moore's method. (Copyright (c) 1993 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)