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On Gap Functions for Multivalued Stampacchia Variational Inequalities

Author

Listed:
  • D. Aussel

    (Université de Perpignan)

  • J. Dutta

    (Indian Institute of Technology)

Abstract

Gap functions have proved to be efficient tools to study single-valued variational inequalities. This approach allows us to reformulate the problem into an optimization problem. New notions of gap functions are defined for set-valued variational inequalities. We prove finiteness and error bounds properties, i.e. upper estimates for the distance to the solution set of the variational inequality.

Suggested Citation

  • D. Aussel & J. Dutta, 2011. "On Gap Functions for Multivalued Stampacchia Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 513-527, June.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:3:d:10.1007_s10957-011-9801-y
    DOI: 10.1007/s10957-011-9801-y
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    References listed on IDEAS

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    1. Joydeep Dutta & Christiane Tammer, 2006. "Lagrangian conditions for vector optimization in Banach spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 521-540, December.
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    Cited by:

    1. D. Aussel & R. Correa & M. Marechal, 2011. "Gap Functions for Quasivariational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 474-488, December.
    2. J. M. Borwein & J. Dutta, 2016. "Maximal Monotone Inclusions and Fitzpatrick Functions," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 757-784, December.
    3. Xiao-bo Li & Li-wen Zhou & Nan-jing Huang, 2016. "Gap Functions and Global Error Bounds for Generalized Mixed Variational Inequalities on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 830-849, March.
    4. Khan, Suhel Ahmad & Chen, Jia-wei, 2015. "Gap function and global error bounds for generalized mixed quasi variational inequalities," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 71-81.
    5. Eleftherios Couzoudis & Philipp Renner, 2013. "Computing generalized Nash equilibria by polynomial programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 459-472, June.

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