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Iterative methods for variational and complementarity problems

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Abstract

In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.

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Author notes

  1. J. S. Pang

    Present address: School of Management and Administration, The University of Texas at Dallas, 75080, Richardson, TX, USA

Authors and Affiliations

  1. Graduate School of Industrial Administration, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    J. S. Pang & D. Chan

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  1. J. S. Pang
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  2. D. Chan
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Additional information

This research was based on work supported by the National Science Foundation under grant ECS-7926320.

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Pang, J.S., Chan, D. Iterative methods for variational and complementarity problems. Mathematical Programming 24, 284–313 (1982). https://doi.org/10.1007/BF01585112

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