Algorithm for generalized multivalued variational inequalities in hilbert spaces

Abstract We introduce a new class of generalized multivalued variational inequality problems (1.1) which contain several existing variational inequality problems as special cases. An iterative algorithm for finding approximate solutions of problem (1.1) is considered. Several convergence results for this algorithm are derived and in particular several existence results of problems (1.1) are obtained. We also introduce a new class of generalized multivalued complementarity problems (5.1) which also contain several known complementarity problems as special cases. It is shown that problem (5.1) is equivalent to problem (1.1) of special type from which several existence results of problem (5.1) are obtained.

[1]  M. Noor.  General variational inequalities , 1988 .

[2]  Muhammad Aslam Noor,et al.  On the nonlinear complementarity problem , 1987 .

[3]  S. Karamardian.  Generalized complementarity problem , 1970 .

[4]  Abul Hasan Siddiqi,et al.  General strongly nonlinear variational inequalities , 1992 .

[5]  Jong-Shenq Guo,et al.  Extension of strongly nonlinear quasivariational inequalities , 1992 .

[6]  G. Habetler,et al.  Existence theory for generalized nonlinear complementarity problems , 1971 .

[7]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[8]  Romesh Saigal,et al.  Extension of the Generalized Complementarity Problem , 1976, Math. Oper. Res..

[9]  Muhammad Aslam Noor,et al.  Quasi variational inequalities , 1988 .

[10]  M. Noor,et al.  Nonlinear quasi complementarity problems , 1989 .

[11]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[12]  Youzhong Guo.  ON VARIATIONAL INEQUALITIES , 1984 .

[13]  M. Noor.  Generalized quasi complementarity problems , 1986 .

[14]  Nan-jing Huang,et al.  Generalized strongly nonlinear quasi-complementarity problems in Hilbert spaces☆ , 1991 .

[15]  Abul Hasan Siddiqi,et al.  Strongly nonlinear quasivariational inequalities , 1990 .

[16]  Jen-Chih Yao,et al.  Applications of Variational Inequalities to Nonlinear Analysis , 1991 .

[17]  Muhammad Aslam Noor,et al.  An Iterative Scheme for a Class of Quasi Variational Inequalities , 1985 .