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A Partial Regularization Method for Saddle Point Seeking

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  • A. Ruszczynski

Abstract

This article generalizes the Nash equilibrium approach to linear programming to the saddle point problem. The problem is shown to be equivalent to a non-zero sum game in which objectives of the players are obtained by partial regularization of the original function. Based on that, a solution method is developed in which the players improve their decisions while anticipating the steps of their opponents. Strong convergence of the method is proved and application to convex optimization is discussed. Note: This document is not complete since some graphics were generated manually and are therefore not included in the online version. For the complete document contact IIASA's Publications department.

Suggested Citation

  • A. Ruszczynski, 1994. "A Partial Regularization Method for Saddle Point Seeking," Working Papers wp94020, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp94020
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    References listed on IDEAS

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    1. 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.
    2. M.J. Kallio & A. Ruszczynski, 1994. "Parallel Solution of Linear Programs Via Nash Equilibria," Working Papers wp94015, International Institute for Applied Systems Analysis.
    3. A. Ruszczynski, 1992. "Augmented Lagrangian Decomposition for Sparse Convex Optimization," Working Papers wp92075, International Institute for Applied Systems Analysis.
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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. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.

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