H-Monotone operator and resolvent operator technique for variational inclusions

Applied Mathematics and Computation

Volumn 145, Issue 2-3, 2003, Pages 795-803

  Fang, Ya ping ^a   Huang, Nan jing ^a  

^a SICHUAN UNIVERSITY   (China)

Author keywords

H Monotone operator; Iterative algorithm; Resolvent operator technique; Variational inclusion

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ITERATIVE METHODS;

RESOLVENT OPERATOR TECHNIQUES;

MATHEMATICAL OPERATORS;

EID: 0043023454     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(03)00275-3     Document Type: Article

References (19)

1. Adly S. Perturbed algorithm and sensitivity analysis for a general class of variational inclusions. J. Math. Anal. Appl. 201:1996;609-630.
2. Baiocchi C., Capelo A. Variational and Quasi-Variational Inequalities, Application to Free Boundary Problems. 1984;Wiley, New York/London.
3. Ding X.P. Perturbed proximal point for generalized quasivariational inclusions. J. Math. Anal. Appl. 210:1997;88-101.
4. Ding X.P., Luo C.L. Perturbed proximal point algorithms for generalized quasi-variational-like inclusions. J. Comput. Appl. Math. 210:2000;153-165.
5. Giannessi F., Maugeri A. Variational Inequalities and Network Equilibrium Problems. 1995;Plenum, New York.
6. Glowinski R. Numerical Methods for Nonlinear Variational Problems. 1984;Springer-Verlag, Berlin.
7. Glowinski R., Lions J.L., Tremolieres R. Numerical Analysis of Variational Inequalities. 1981;North-Holland, Amsterdam.
8. Harker P.T., Pang J.S. Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Program. 48:1990;161-220.
9. Hassouni A., Moudafi A. A perturbed algorithm for variational inequalities. J. Math. Anal. Appl. 185:1994;706-712.
10. Huang N.J. Generalized nonlinear variatonal inclusions with noncompact valued mappings. Appl. Math. Lett. 9(3):1996;25-29.
11. Huang N.J. Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions. Comput. Math. Appl. 35(10):1998;1-7.
12. Huang N.J. A new completely general class of variational inclusions with noncompact valued mappings. Comput. Math. Appl. 35(10):1998;9-14.
13. Huang N.J., Deng C.X. Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities. J. Math. Anal. Appl. 256:2001;345-359.
14. Kazmi K.R. Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions. J. Math. Anal. Appl. 209:1997;572-584.
15. Lee C.H., Ansari Q.H., Yao J.C. A perturbed algorithm for strongly nonlinear variational-like inclusions. Bull. Aust. Math. Soc. 62:2000;417-426.
16. Noor M.A. Some recent advances in variational inequalities I. New Zeal. J. Math. 26:1997;53-80. (II, 229-255).
17. Stampacchia G. Formes bilineaires sur les ensemble convexes. C.R. Acad. Sci. Paris. 258:1964;4413-4416.
18. Yuan G.X.Z. KKM Theory and Applications in Nonlinear Analysis. 1999;Marcel-Dekker, New York.
19. Zeidler E. Nonlinear Functional Analysis and its Applications II: Monotone Operators. 1985;Springer-Verlag, Berlin.