an:01698913
Zbl 1013.49005
Yamada, Isao
The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings
EN
Butnariu, Dan (ed.) et al., Inherently parallel algorithms in feasibility and optimization and their applications. Research workshop, Haifa, Israel, March 13-16, 2000. Amsterdam: North-Holland/ Elsevier. Stud. Comput. Math. 8, 473-504 (2001).
2001
a
49J40 47H10 47J20 65K10 47H09
variational inequality; fixed point set; hybrid steepest descent method
This paper presents a simple algorithmic solution to the variational inequality problem defined over the nonempty intersection of multiple fixed point sets of nonexpansive mappings in a real Hilbert space. The algorithmic solution is named the hybrid steepest descent method and generates a sequence strongly convergent to the solution of the problem.
The applicability of this method to the convexly constrained generalized pseudoinverse problem as well as to the convex feasibility problem is demonstrated by constructing nonexpansive mappings whose fixed point sets are the feasible sets of the problem.
For the entire collection see [Zbl 0971.00058].
Ruxandra Stavre (Bucure??ti)