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Parallel Solution of Linear Programs Via Nash Equilibria

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  • M.J. Kallio
  • A. Ruszczynski

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.

Suggested Citation

  • M.J. Kallio & A. Ruszczynski, 1994. "Parallel Solution of Linear Programs Via Nash Equilibria," Working Papers wp94015, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp94015
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    References listed on IDEAS

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    1. A. Ruszczynski, 1992. "Augmented Lagrangian Decomposition for Sparse Convex Optimization," Working Papers wp92075, International Institute for Applied Systems Analysis.
    2. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    3. Robert E. Bixby, 1992. "Implementing the Simplex Method: The Initial Basis," INFORMS Journal on Computing, INFORMS, vol. 4(3), pages 267-284, August.
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    Cited by:

    1. M.J. Kallio & A. Ruszczynski, 1994. "Perturbation Methods for Saddle Point Computation," Working Papers wp94038, International Institute for Applied Systems Analysis.
    2. A. Ruszczynski, 1994. "A Partial Regularization Method for Saddle Point Seeking," Working Papers wp94020, International Institute for Applied Systems Analysis.
    3. M.J. Kallio & C.H. Rosa, 1994. "Large-Scale Convex Optimization via Saddle Point Computation," Working Papers wp94107, International Institute for Applied Systems Analysis.

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