Parallel Solution of Linear Programs Via Nash Equilibria

M.J. Kallio and Andrzej Ruszczynski ()

Working Papers from International Institute for Applied Systems Analysis

Abstract: The linear programming problem is shown to be equivalent to a game in which primal players minimize the augmented Lagrangian function for the primal problem and dual players maximize the augmented Lagrangian function for the dual problem. Based on that, a parallel solution method is developed in which processors carry out under-relaxed Jacobi steps for the players. Strong convergence of the method is proved and the ratio of linear convergence estimated. Computational results are highly encouraging.

Date: 1994-03
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