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Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems

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  • L.R. Huang

    (South China Normal University)

  • K. F. Ng

    (Chinese University of Hong Kong)

Abstract

We investigate whether some merit functions for variational inequality problems (VIP) provide error bounds for the underlying VIP. Under the condition that the involved mapping F is strongly monotone, but not necessarily Lipschitz continuous, we prove that the so-called regularized gap function provides an error bound for the underlying VIP. We give also an example showing that the so-called D-gap function might not provide error bounds for a strongly monotone VIP.

Suggested Citation

  • L.R. Huang & K. F. Ng, 2005. "Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 299-314, May.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:2:d:10.1007_s10957-004-1839-7
    DOI: 10.1007/s10957-004-1839-7
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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.
    2. Y. B. Zhao & J. Y. Han & H. D. Qi, 1999. "Exceptional Families and Existence Theorems for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 475-495, May.
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    Cited by:

    1. Suhel Ahmad Khan & Jia-Wei Chen, 2015. "Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 767-776, September.
    2. Bui Dinh & Tien-Son Pham, 2022. "Error Bounds of Regularized Gap Functions for Polynomial Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 226-247, January.
    3. 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.
    4. K. F. Ng & L. L. Tan, 2007. "D-Gap Functions for Nonsmooth Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 77-97, April.

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