Bundle-based decomposition for large-scale convex optimization: Error estimate and application to block-angular linear programs

Robinson has proposed the bundle-based decomposition algorithm to solve a class of structured large-scale convex optimization problems. In this method, the original problem is transformed (by dualization) to an unconstrained nonsmooth concave optimizatin problem which is in turn solved by using a modified bundle method. The paper gives a posterior error estimates on the approximate primal optimal solution and on the duality gap. It describes implementation and present computational experience with a special case of this class of problems, namely, block-angular linear programming problems. The paper observes that the method is efficient in obtaining the approximate optimal solution and compares favorable with MINOS and an advanced implementation of the Dantzig-Wolfe decomposition method.