The paper proposes a modification of cross decomposition, called mean value cross decomposition, for linear programming problems. The method is a generalization of the Kornai-Liptak method, and eliminates the need for using master problems. The base for the method is the subproblem phase in cross decomposition, where it iterates between the dual subproblem and the primal subproblem. However, instead of using the last solution of one subproblem as input to the other and vice versa, the paper uses the average (mean value) of all previously obtained solutions. It shows that this is equivalent to the Brown-Robinson method for a matrix game, and use this fact to prove convergence of the procedure. Finally, the paper presents some computational results, comparing this method to other primal-dual methods and to using a standard LP code.
