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Convergence and Error Bound of a Method for Solving Variational Inequality Problems via the Generalized D-Gap Function

Author

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  • B. Qu

    (Qufu Normal University)

  • C. Y. Wang

    (Qufu Normal University)

  • J. Z. Zhang

    (City University of Hong Kong)

Abstract

The variational inequality problem (VIP) can be reformulated as an unconstrained minimization problem through the generalized D-gap function. Recently, a hybrid Newton-type method was proposed by Peng and Fukushima for minimizing a special form of the generalized D-gap function. In this paper, the hybrid Newton-type algorithm is extended to minimize the general form g αβ of the generalized D-gap function. It is shown that the algorithm has nice convergence properties. Under some reasonable conditions, it is proved that the algorithm is locally and globally convergent. Moreover, it is proved that the function g αβ has bounded level sets for strongly monotone VIP. An error bound of the algorithm is obtained.

Suggested Citation

  • B. Qu & C. Y. Wang & J. Z. Zhang, 2003. "Convergence and Error Bound of a Method for Solving Variational Inequality Problems via the Generalized D-Gap Function," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 535-552, December.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:3:d:10.1023_b:jota.0000006688.13248.04
    DOI: 10.1023/B:JOTA.0000006688.13248.04
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.

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