Parallel algorithms for variational inequalities over the Cartesian product of the intersections of the fixed point sets of nonexpansive mappings

Authors:
Noriyuki Takahashi;Isao Yamada
Affiliations:
Department of Communications and Integrated Systems, Tokyo Institute of Technology, S3-60, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan;Department of Communications and Integrated Systems, Tokyo Institute of Technology, S3-60, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
Venue:
Journal of Approximation Theory
Year:
2008

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Abstract

This paper presents a framework of iterative algorithms for the variational inequality problem over the Cartesian product of the intersections of the fixed point sets of nonexpansive mappings in real Hilbert spaces. Strong convergence theorems are established under a certain contraction assumption with respect to the weighted maximum norm. The proposed framework produces as a simplest example the hybrid steepest descent method, which has been developed for solving the monotone variational inequality problem over the intersection of the fixed point sets of nonexpansive mappings. An application to a generalized power control problem and numerical examples are demonstrated.