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On the Gap Functions of Prevariational Inequalities

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  • X.Q. Yang

    (Hong Kong Polytechnic University)

Abstract

Gap functions play a crucial role in transforming a variational inequality problem into an optimization problem. Then, methods solving an optimization problem can be exploited for finding a solution of a variational inequality problem. It is known that the so-called prevariational inequality is closely related to some generalized convex functions, such as linear fractional functions. In this paper, gap functions for several kinds of prevariational inequalities are investigated. More specifically, prevariational inequalities, extended prevariational inequalities, and extended weak vector prevariational inequalities are considered. Furthermore, a class of gap functions for inequality constrained prevariational inequalities is investigated via a nonlinear Lagrangian.

Suggested Citation

  • X.Q. Yang, 2003. "On the Gap Functions of Prevariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 437-452, February.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:2:d:10.1023_a:1022422407705
    DOI: 10.1023/A:1022422407705
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    References listed on IDEAS

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    1. C. J. Goh & X. Q. Yang, 2001. "Nonlinear Lagrangian Theory for Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 99-121, April.
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    Cited by:

    1. D. L. Zhu & L. L. Zhu & Q. Xu, 2008. "Generalized Invex Monotonicity and Its Role in Solving Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 453-464, May.
    2. J. Li & G. Mastroeni, 2010. "Vector Variational Inequalities Involving Set-valued Mappings via Scalarization with Applications to Error Bounds for Gap Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 355-372, May.
    3. N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    4. T. Antczak, 2007. "Saddle-Point Criteria in an η-Approximation Method for Nonlinear Mathematical Programming Problems Involving Invex Functions," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 71-87, January.

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