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Extended Projection Methods for Monotone Variational Inequalities

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  • Y. B. Zhao

    (Chinese Academy of Sciences)

Abstract

In this paper, we prove that each monotone variational inequality is equivalent to a two-mapping variational inequality problem. On the basis of this fact, a new class of iterative methods for the solution of nonlinear monotone variational inequality problems is presented. The global convergence of the proposed methods is established under the monotonicity assumption. The conditions concerning the implementability of the algorithms are also discussed. The proposed methods have a close relationship to the Douglas–Rachford operator splitting method for monotone variational inequalities.

Suggested Citation

  • Y. B. Zhao, 1999. "Extended Projection Methods for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 219-231, January.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:1:d:10.1023_a:1021781318170
    DOI: 10.1023/A:1021781318170
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    References listed on IDEAS

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    1. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
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