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Derivative-Free Methods for Monotone Variational Inequality and Complementarity Problems

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  • J. M. Peng

    (Delft University of Technology)

Abstract

Monotone variational inequality problems with box constraints and complementarity problems are reformulated as simple-bound optimization problems. Some derivative-free methods for these problems are proposed. It is shown that, for these new methods, the updated point sequence remains feasible with respect to its simple constraints if the initial point is feasible. Under certain conditions, these methods are globally convergent.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:1:d:10.1023_a:1021712513685
    DOI: 10.1023/A:1021712513685
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    References listed on IDEAS

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    1. J. M. Peng, 1997. "Convexity of the Implicit Lagrangian," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 331-341, February.
    2. C. Kanzow & N. Yamashita & M. Fukushima, 1997. "New NCP-Functions and Their Properties," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 115-135, July.
    3. N. Yamashita & K. Taji & M. Fukushima, 1997. "Unconstrained Optimization Reformulations of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 439-456, March.
    4. 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.
    5. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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