SOME NONLINEAR VARIATIONAL INEQUALITIES

Article Sidebar

PDF
Published: Jun 1, 1995
DOI: https://doi.org/10.5556/j.tkjm.26.1995.4382
Keywords:
Variational inequalities auxiliary principle optimization problems.

Main Article Content

MUHAMMAD ASLAM NOOR
Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.

Abstract




In this paper, we introduce and study a new class of variational in- equalities. Using the auxiliary principle technique, we prove the existence of a solution of this class of variational inequalities and suggest a new and novel itera- tive algorithm. Several special cases, which can be obtained from the main results, are also discussed.




Article Details

How to Cite
NOOR, M. A. (1995). SOME NONLINEAR VARIATIONAL INEQUALITIES. Tamkang Journal of Mathematics, 26(2), 97–105. https://doi.org/10.5556/j.tkjm.26.1995.4382
Issue
Vol. 26 No. 2 (1995)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

C. Baiocchi and A. Capelo, Variational and quasi-variational inequalities, J. Wiley and Sons, New York, 1984.

J. Crank, Free and moving boundary problems, Clarendon Press, Oxford, U.K. 1984.

E. Blum and W. Oettli, "From optimization and variational inequalities to equilibrium problems," Math. Student, 63 (1994), 123-145.

S. Dafermos, "Exchange price equilibria and variational inequalities," Math. Programming, 46 (1990), 391-402.

M. Fukushima, "Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems," Mathematical Programming, 53 (1992), 99-110.

R. Glowinski, J.L. Lions and R. Tremolieres, Numerical analysis of variational inequalities, North- Holland, Amsterdam, 1981.

R. Glowinski, Numerical methods for nonlinear variational problems, Springer-Verlag, Berlin, New York, 1985.

G. Isac, "A special variational inequality and the implicit complementarity problem," J. Fae. Sci. Univ. Tokyo, 37 (1990), 109-127.

N. Kikuchi and J.T . Oden, Contact problems in elasticity, SIAM Publishing Co., Philadelphia, 1988.

D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their appli- cations, Academic Press, London, New York, 1980.

T. Larsson and M. Patriksson, "A class of gap functions for variational inequalities," Mathematical Programming, 64 (1994), 53-79.

M. Aslam Noor, "Quasi variational inequalities," Appl. Math. Lett., 1 (1988), 367-370.

M. Aslam Noor, "General nonlinear variational inequalities," J. Math. Anal. Appl., 158 (1987), 78-84.

M. Aslam Noor, "An iterative algorithm for nonlinear variational inequalities," Appl. Math. Lett., 5 (4) (1992), 11-14.

M. Aslam Noor, On variational inequalities, Ph.D. Thesis, Brunel University, Greater London, U.K. 1975.

M. Aslam Noor, "General auxiliary principle for variational inequalities," PanAmer. Math. J., (1) (1994), 27-44.

M. Aslam Noor, "Equivalence of differentiable optimization problems for variational inequalities," J. Natural Geometry, 8 (1995).

M. Aslam Noor, On Iterative algorithms for a class of nonlinear variational inequalities, Approx. Theory Appl. (1994), in Press.

M. Aslam Noor, K. lnayat Noor and Th.M. Rassias, "Some aspects of variational inequalities," J. Comput. Appl. Math., 47 (1993), 285-312.

W. Oettli, Some remarks on general nonlinear complementarity problems, Preprint, University of Mannheim, Germany, 1987.

J. F. Rodrigues, Obstacle problems in mathematical physics, North-Holland, Amsterdam, 1987.

D. L. Zhu and P. Marcotte, "An extended descent framework for variational inequalities," J. Optim. Theory Appl. 80(1994), 329- 366.