On a class of multivalued variational inequalities

Journal of Applied Mathematics and Stochastic Analysis

Volumn 11, Issue 1, 1998, Pages 79-93

  Noor, Muhammad Aslam ^a  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Algorithms; Auxiliary Principle; Convergence Criteria; Fixed Point Problem; Optimization Problems; Variational Inequalities; Wiener Hopf Equations

Indexed keywords

EID: 54649083625     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/S1048953398000070     Document Type: Article

References (40)

1. Baiocchi, C. and Capelo, A., Variational and Quasi-Variational Inequalities, J. Wiley and Sons, New York 1984.
2. Blum, E. and Oettli, W., From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994), 123-145.
3. Chang, S.S. and Huang, N.J., Generalized strongly nonlinear quasi-complementarity problems in Hilbert spaces, J. Math. Anal. Appl. 158 (1991), 194-202.
4. Cohen, G., Auxiliary problem extended to variational inequalities, J. Optim. Theor. Appl. 59 (1988), 325-333.
5. Cottle, R.W., Giannessi, F. and Lions, J.L., Variational Inequalities and Complementarity Problems: Theory and Applications, J. Wiley and Sons, New York 1980.
6. Crank, J., Free and Moving Boundary Problems, Clarendon Press, Oxford 1984.
7. Ding, X.P., Generalized strongly nonlinear quasi-variational inequalities, J. Math. Anal. Appl. 173 (1993), 577-587.
8. Fang, S.C. and Peterson, E.L., Generalized variational inequalities, J. Optim. Theory. Appl. 38 (1982), 363-383.
9. Giannessi, F. and Maugeri, A., Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York 1995.
10. Glowinski, R., Lions, J.L. and Tremolieres, R., Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam 1981.
11. Fukushima, F., Equivalent differential optimization problems and descent methods for a symmetric variational inequality problems, Math. Program. 53 (1992), 99-110.
12. Harker, P.T. and Pang, J.S., Finite dimensional variational inequality and nonlinear complementarity problems; a survey of theory, algorithms and applications, Math. Programming 48 (1990), 161-220.
13. Jou, C.R. and Yao, Y.C., Algorithms for generalized multivalued variational inequalities in Hilbert spaces, Computer Math. Appl. 25:9 (1993), 7-16.
14. Kinderlehrer, D. and Stampacchia, G., An Introduction to Variational Inequalities and Their Applications, Academic Press, New York 1980.
15. Larsson, T. and Patriksson, M., A class of gap functions for variational inequality, Math. Program 64 (1994), 53-79.
16. Lions, J.L. and Stampacchia, G., Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493-519.
17. Noor, M.A., Rieśz-Frèchet Theorem and Monotonicity, M.Sc. Thesis, Queen's University, Kingston, Ontario, Canada 1971.
18. Noor, M.A., Some recent advances in variational inequalities (I, II), N.J. Math. 26 (1997).
19. Noor, M.A., Theory of variational inequalities, Lecture Notes, Mathematics Department, King Saud University, Riyadh, Saudi Arabia 1996.
20. Noor, M.A., On Variational Inequalities, Ph.D. Thesis, Brunel University, London, England, UK 1975.
21. Noor, M.A., An iterative algorithm for variational inequalities, J. Math. Anal. Appl. 158 (1991), 448-455.
22. Noor, M.A., On certain class of variational inequalities and related iterative algorithms, J. Appl. Math. Stoch. Anal. 9 (1996), 43-56.
23. Noor, M.A., Multivalued strongly nonlinear variational inequalities, Optimization 36 (1996), 31-39.
24. Noor, M.A., Noor, K.I., and Rassias, Th.M., Some aspects of variational inequalities, J. Comput. Appl. Math. 47 (1993), 285-312.
25. Noor, M.A., Noor, K.I. and Rassias, Th.M., Invitation to variational inequalities, In: Analysis, Geometry and Groups: A Riemann Legacy Volume (ed. by H.M. Srivastava and Th.M. Rassias), Hadronic Press, USA (1993), 373-448.
26. Noor, M.A. and Oettli, W., On general nonlinear complementarity problems and quasi-equilibria, Le Matematiche 49 (1994), 373-448.
27. Noor, M.A., Variational inequalities in physical oceanography, In: Ocean Waves Engineering, (ed. by M. Rahman), Comput. Mechanics Publications, Southampton, UK (1994), 201-226.
28. Noor, M.A., Generalized multivalued variational inequalities, Dynamic Systems Appl. 4 (1995), 469-476.
29. Panagiotopoulos, P.D. and Stavroulakis, G.E., New types of variational principles based on the notion of quasidifferentiability, Acta Mechanica 94 (1992), 171-194.
30. Panagiotopoulos, P.D., Inequality Problems in Mechanics and Applications, Birkhauser, Boston 1985.
31. Parida, J. and Sen, A., Duality and existence theory for nondifferentiable programming, J. Optim. Theory Appl. 48 (1986), 451-458.
32. Parida, J. and Sen, A., A variational-like inequality for multifunctions with applications, J. Math. Anal. Appl. 124 (1987), 73-81.
33. Pitonyak, A., Shi, P. and Shillor, M., On an iterative method for variational inequalities, Numerische Math. 58 (1990), 231-242.
34. Shi, P., Equivalence of variational inequalities with Wiener-Hopf equations, Proc. Amer. Math. Soc. 111 (1991), 339-346.
35. Shi, P., An iterative method for obstacle problems via Green's functions, Nonlinear Analysis 15 (1990), 339-344.
36. Shih, M.H. and Tan, K.K., Browder-Hartman-Stampacchia variational inequalities for multivalued monotone operators, J. Math. Anal. Appl. 134 (1988), 431-440.
37. Speck, F.O., General Wiener-Hopf Factorization Methods, Pitman Advanced Publishing Program, London 1985.
38. Stampacchia, G., Formes bilineaires coercitives sur les ensembles convexes, C.R. Acad. Sci. Paris 285 (1964), 4413-4416.
39. Yao, J.C., The generalized quasi-variational inequality problem with applications, J. Math. Anal. Appl. 158 (1991), 139-160.
40. Zhu, D.L. and Marcotte, P., An extended descent framework for variational inequalities, J. Optim. Theory Appl. 80 (1994), 349-366.