Advertisement

Variational inequalities with nonmonotone operators

  • J. S. Guo
  • J. C. Yao
Contributed Papers

Abstract

In this paper, existence results on variational inequalities and generalized variational inequalities for some nonmonotone operators over closed convex subsets of a real reflexive Banach space are proved. In particular, some surjectivity results and applications to complementarity and generalized complementarity problems are given.

Key Words

Variational inequalities generalized variational inequalities nonmonotone operators surjectivity complementarity problems generalized complementarity problems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Browder, F. E.,Existence Theorems for Nonlinear Partial Differential Equations, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence, Rhode Island, Vol. 16, pp. 1–60, 1970.Google Scholar
  2. 2.
    Browder, F. E.,Pseudo-Monotone Operators and the Direct Method of the Calculus of Variations, Archive for Rational Mechanic and Analysis, Vol. 38, pp. 268–277, 1970.Google Scholar
  3. 3.
    Browder, F. E.,Fixed-Point Theory and Nonlinear Problems, Bulletin of the American Mathematical Society, Vol. 9, pp. 1–39, 1983.Google Scholar
  4. 4.
    Browder, F. E.,On the Unification of the Calculus of Variations and the Theory of Monotone Nonlinear Operators in Banach Spaces, Proceedings of the National Academy of Sciences, USA, Vol. 56, pp. 419–425, 1966.Google Scholar
  5. 5.
    Cottle, R. W., andYao, J. C.,Pseudomonotone Complementarity Problems in Hilbert Space, Journal of Optimization Theory and Applications, Vol. 75, pp. 281–295, 1992.Google Scholar
  6. 6.
    Théra, M.,A Note on the Hartman-Stampacchia Theorem, Proceedings of the International Conference on Nonlinear Analysis and Applications, Edited by V. Lakshmikantham, Marcel Dekker, New York, New York, pp. 573–577, 1987.Google Scholar
  7. 7.
    Browder, F. E., andHess, P.,Nonlinear Mappings of Monotone Type in Banach Spaces, Journal of Functional Analysis, Vol. 11, pp. 251–294, 1972.Google Scholar
  8. 8.
    Kravvaritis, D.,Nonlinear Equations and Inequalities in Banach Spaces, Journal of Mathematical Analysis and Applications, Vol. 67, pp. 205–214, 1979.Google Scholar
  9. 9.
    Mosco, U.,A Remark on a Theorem of F. E. Browder, Journal of Mathematical Analysis and Applications, Vol. 20, pp. 90–93, 1967.Google Scholar
  10. 10.
    Stampacchia, G.,Variational Inequalities, Theory and Applications of Monotone Operators, Edited by A. Ghizzetti, Edizioni Oderisi, Gubbio, Italy, pp. 101–192, 1969.Google Scholar
  11. 11.
    Karamardian, S.,Generalized Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 8, pp. 161–168, 1971.Google Scholar
  12. 12.
    Harker, P. T., andPang, J. S.,Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48B, pp. 161–220, 1990.Google Scholar
  13. 13.
    Bazaraa, M. S., Goode, J. J., andNashed, M. Z.,A Nonlinear Complementarity Problem in Mathematical Programming in Banach Space, Proceedings of the American Mathematical Society, Vol. 35, pp. 165–170, 1972.Google Scholar
  14. 14.
    Saigal, R.,Extension of the Generalized Complementarity Problem, Mathematics of Operations Research, Vol. 1, pp. 260–266, 1976.Google Scholar
  15. 15.
    Luna, G.,A Remark on the Nonlinear Complementarity Problem, Proceedings of the American Mathematical Society, Vol. 48, pp. 132–134, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • J. S. Guo
    • 1
  • J. C. Yao
    • 2
  1. 1.Institute of Applied MathematicsNational Tsing Hua UniversityHsinchuTaiwan, ROC
  2. 2.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan, ROC

Personalised recommendations