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Perturbation Methods for Saddle Point Computation

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  • M.J. Kallio
  • A. Ruszczynski

Abstract

A general class of iterative methods for saddle point seeking is developed. The directions used are subgradients evaluated at perturbed points. Convergence of the methods is proved and alternative strategies for implementation are discussed. The procedure suggests scalable algorithms for solving large-scale linear programs via saddle points. For illustration, some encouraging tests with the standard Lagrangian of linear programs from the Netlib library are reported.

Suggested Citation

  • M.J. Kallio & A. Ruszczynski, 1994. "Perturbation Methods for Saddle Point Computation," Working Papers wp94038, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp94038
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    File URL: http://www.iiasa.ac.at/Publications/Documents/WP-94-038.ps
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    References listed on IDEAS

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    1. A. Ruszczynski, 1994. "A Partial Regularization Method for Saddle Point Seeking," Working Papers wp94020, International Institute for Applied Systems Analysis.
    2. M.J. Kallio & A. Ruszczynski, 1994. "Parallel Solution of Linear Programs Via Nash Equilibria," Working Papers wp94015, International Institute for Applied Systems Analysis.
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    Cited by:

    1. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    2. S.D. Flam & A. Ruszczynski, 1994. "Noncooperative Convex Games: Computing Equilibrium By Partial Regularization," Working Papers wp94042, International Institute for Applied Systems Analysis.
    3. Wenjie Zhao & Guangming Zhou, 2022. "Local saddle points for unconstrained polynomial optimization," Computational Optimization and Applications, Springer, vol. 82(1), pages 89-106, May.
    4. A. Nedić & A. Ozdaglar, 2009. "Subgradient Methods for Saddle-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 205-228, July.
    5. Maarit Kallio & Markku Kallio, 2002. "Nonparametric Methods for Evaluating Economic Efficiency and Imperfect Competition," Journal of Productivity Analysis, Springer, vol. 18(2), pages 171-189, September.
    6. 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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    1. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    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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