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Global Method for Monotone Variational Inequality Problems with Inequality Constraints

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  • J. M. Peng

    (Academia Sinica)

Abstract

We consider optimization methods for monotone variational inequality problems with nonlinear inequality constraints. First, we study the mixed complementarity problem based on the original problem. Then, a merit function for the mixed complementarity problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original variational inequality problem is reformulated as simple bounded minimization. Under certain assumptions, we show that any stationary point of the optimization problem is a solution of the problem considered. Finally, we propose a descent method for the variational inequality problem and prove its global convergence.

Suggested Citation

  • J. M. Peng, 1997. "Global Method for Monotone Variational Inequality Problems with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 419-430, November.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:2:d:10.1023_a:1022695523877
    DOI: 10.1023/A:1022695523877
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    References listed on IDEAS

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    1. Jong-Shi Pang, 1990. "Newton's Method for B-Differentiable Equations," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 311-341, May.
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    Cited by:

    1. J. M. Peng, 1998. "Derivative-Free Methods for Monotone Variational Inequality and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 235-252, October.

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