On a dual method for a specially structured linear programming problem with application to stochastic programming

The paper revises and improves on a Dual Type Method DTM devel oped by A Pr ekopa in two ways The rst improvement allows us in each iteration to perform the largest step toward the optimum The second inprovement consists of exploting the structure of the working basis which has to be inverted in each iteration of the DTM and updating its inverse in product form as it is usual in case of the standard dual method Acknowledgements The rst author gratefully acknowledge the support of the Kommis sion f ur die F orderung von Nachwuchswissentschaftlerinnen der FU Berlin The third author gratefully acknowledges the support of the Foundation for the Devel opment of Higher Education in Hungary project III