General nonlinear mixed variational-like inequalities

Optimization

Volumn 37, Issue 4, 1996, Pages 357-367

  Aslam Noor, M ^a  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Auxiliary principle; Iterative algorithm; Variational like inequalities

Indexed keywords

EID: 0030471159     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331939608844227     Document Type: Article

References (36)

1. Auchumuty, G. (1989). Variational principles for variational inequalities, Numer. Functional Anal. Optim. 10, 863-874
2. Baiocchi, C. and Capelo, A. (1984). Variational and Quasi Variational Inequalities, J. Wiley and sons, New York, 1984
3. Blum, E. and Oettli, W. (1994). From optimization and variational inequalities to equilibrium problems, Math. Student, 63, 123-145
4. Cohen, G. (1988). Auxiliary problem principle extended to variational inequalities, J. Optim. Ther. Appl. 59, 325-333
5. Cottle, R. W., Pang J. S. and Stone, R. E. (1992). The Linear Complementarity Problem, Academic Press, New York.
6. Crank, J. F. (1984). Free and Moving Boundary Problems, Clarendon Press, Oxford, U.K.
7. Dien, N. H. (1992). Some Remarks on variatonal-like and quasi variational-like inequalities, Bull. Austral. Math. Soc. 46, 335-342
8. Fukushima, M. (1992). Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Mathematical Programming 53, 99-110
9. Giannessi, F. and Maugeri, A. (Editors), (1995). Variational Inequalities and Network Equilibrium, Plenum Press, New York.
10. Glowmski, R., Lions J. L. and Trèmolières, R. (1981). Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam.
11. Harker, P. T. and Pang, J. S. (1990). Finite dimensional variational inequality and nonlinear complementarity applicaitons: a survey of theory, algorithms and applicaitons, Math. Program. 48, 161-220
12. Kikuchi, N. and Oden, J. T. (1988). Contact Problems in Elasticity, SIAM Publishing Co., Philadelphia, U.S.A.
13. Larsson, T. and Patriksson, M. A class of gap funcitons for variational inequalities, Mathematical Programming, 64 (1994), 53-79
14. Lions, J. L. and Stampacchia, G. (1967). Variational inequalities, Comm. Pure Appl. Math. 20, 493-519
15. Aslam Noor, M. (1987). General nonlinear variational inequaliteis, (1987). J. Math. Anal. Appl. 126, 78-84
16. Aslam Noor, M. (1992). An iterative algorithm for nonlinear variational inequaliteis, Appl. math. Letters 5 (4) 11-14
17. Aslam Noor, M. (1994). General auxiliary principle for variational inequalities, PanAmer. Math. J. 4, (1) 27-44
18. Aslam Noor, M. (1994). Variational-like inequalities, Optimization, 30 323-330
19. Aslam Noor, M. (1996). Preinvex functions and variational inequaliteis, J. Nat. Geometry, 9, 63-67
20. Aslam Noor, M. (1995). Nonconvex functions and variaitonal inequaliteis, J. Optim. Theory Appl. 87, 615-630
21. Aslam Noor, M. (1995). On iterative algorithms for a class of nonlinear variational inequalities, Approx. Theory Appl. 11(3), 95-105.
22. Aslam Noor, M. (1995). Equivalence of differentiate optimization problems for variational inequaliteis, J. Nat. Geometry 8, 177-128
23. Aslam Noor, M. (1975). On Variational Inequalities, Ph.D. Thesis, Brunel University, London, U.K.
24. Aslam Noor, M. Theory of Variational Inequalities, Lecture Notes, Mathematics Department, King Saud University, Riyadh, 1996
25. Aslam Noor, M. (1993). General algorithm for variational inequalities (I), Math. Japonica, 38, 47-53
26. Aslam Noor, M., Inayat Noor, K. and Rassias, Th.M. (1993). Some aspects of variational inequalities, J. Comput. Appl. Math. 47, 285-312
27. Aslam Noor, M., Inayat Noor, K. and Rassias, Th.M. (1993). Invitation to variational inequalities, in: Analysis, Geometry and Groups: A Riemann Legacy Volume, (eds.), Srivastava, H. M. and Th.M Rassias, Hadronic Press, U.S.A. 373-448
28. Aslam Noor, M. and Oettli, W. (1994). On general nonlinear complementarity problems and quasi-equlibria, Le Matematiche, 49, 313-331
29. Panagiotopoulos, P.D. (1985). Inequality Problems in Mechanics and Appliaitons, Birkhäuser, Boston.
30. Stampacchia, G. (1964). Formes bilinéaires coercitives sur les ensembles convexes, C. R. Acad. Sci. Paris, 258, 4413-4416
31. Taji, K. Fukushima, M. and Ibaraki, T. (1993). A globally convergent Newton method for solving strongly monotone variational inequaliteis, Mathematical Programming, 58, 369-383
32. Weir, T. and Jeyakumar, V. (1988). A class of nonconvex functions and mathematical programming, Bull. Austral. Math. Soc. 38, 177-189
33. Weir, T. and Mond, B. (1988). Preinvex functions in multiple objective optimization, J. Math. Anal. Appl. 136, 29-38
34. Yang, X. Q. and Chen, G. Y. (1992). A class of nonconvex functions and pre-variational inequalities, J. Math. Anal. Appl. 169, 359-373
35. Yao, J. C. (1991). The generalized quasi variational inequality problem with applications, J. Math. Anal. Appl 158, 139-160
36. Zhu, D. L. and Marcotte, P. (1994). An extended descent frame work for varitional inequaliteis, J. Optim. Theory Appl. 80, 349-366