On modified hybrid steepest-descent methods for general variational inequalities

Abstract: We consider the general variational inequality , where F and g are mappings from a Hilbert space into itself and C is intersection of the fixed point sets of a finite family of nonexpansive mappings. We suggest and analyze an iterative algorithm with variable parameters as follows: The sequence is shown to converge in norm to the solutions of the general variational inequality under some mild conditions. Application to constrained generalized pseudo-inverse is included. Since the general variational inequalities include variational inequalities, quasi-variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]