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Exceptional Families of Elements for Variational Inequalities in Banach Spaces

Author

Listed:
  • M. Bianchi

    (Università Cattolica del Sacro Cuore)

  • N. Hadjisavvas

    (University of the Aegean)

  • S. Schaible

    (University of California)

Abstract

In keeping with very recent efforts to establish a useful concept of an exceptional family of elements for variational inequality problems rather than complementarity problems as in the past, we propose such a concept. It generalizes previous ones to multivalued variational inequalities in general normed spaces and allows us to obtain several existence results for variational inequalities corresponding to earlier ones for complementarity problems. Compared with the existing literature, we consider problems in more general spaces and under considerably weaker assumptions on the defining map.

Suggested Citation

  • M. Bianchi & N. Hadjisavvas & S. Schaible, 2006. "Exceptional Families of Elements for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 23-31, April.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:1:d:10.1007_s10957-006-9041-8
    DOI: 10.1007/s10957-006-9041-8
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    References listed on IDEAS

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    1. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. M. Bianchi & N. Hadjisavvas & S. Schaible, 2004. "Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 1-17, July.
    3. J. Han & Z. H. Huang & S. C. Fang, 2004. "Solvability of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 501-520, September.
    4. G. Isac & V. V. Kalashnikov, 2001. "Exceptional Family of Elements, Leray–Schauder Alternative, Pseudomonotone Operators and Complementarity," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 69-83, April.
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    Cited by:

    1. J. H. Fan & X. G. Wang, 2009. "Solvability of Generalized Variational Inequality Problems for Unbounded Sets in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 59-74, October.
    2. Y. Chiang, 2010. "Variational inequalities on weakly compact sets," Journal of Global Optimization, Springer, vol. 46(3), pages 465-473, March.
    3. Ren-you Zhong & Huan-xia Lian & Jiang-hua Fan, 2013. "Exceptional Families of Elements for Optimization Problems in Reflexive Banach Spaces with Applications," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 341-359, November.
    4. Y. Chiang, 2010. "Vectorial exceptional families of elements," Journal of Global Optimization, Springer, vol. 47(1), pages 53-62, May.
    5. Wenjie Mu & Jianghua Fan, 2022. "Existence results for solutions of mixed tensor variational inequalities," Journal of Global Optimization, Springer, vol. 82(2), pages 389-412, February.

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