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Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem

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Abstract

Necessary and sufficient conditions are established for the convergence of various iterative methods for solving the linear complementarity problem. The fundamental tool used is the classical notion of matrix splitting in numerical analysis. The results derived are similar to some well-known theorems on the convergence of iterative methods for square systems of linear equations. An application of the results to a strictly convex quadratic program is also given.

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Authors and Affiliations

  1. School of Management and Administration, University of Texas at Dallas, Richardson, Texas

    J. S. Pang (Associate Professor)

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  1. J. S. Pang
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Additional information

Communicated by O. L. Mangasarian

This research was based on work supported by the National Science Foundation under Grant No. ECS-81-14571.

The author gratefully acknowledges several comments by K. Truemper on the topics of this paper.

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Pang, J.S. Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem. J Optim Theory Appl 42, 1–17 (1984). https://doi.org/10.1007/BF00934130

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