Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization
1 Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2 Department of Applied Mathematics, Chung Yuan Christian University, Chung Li 32023, Taiwan
3 Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan
Fixed Point Theory and Applications 2012, 2012:29 doi:10.1186/1687-1812-2012-29Published: 27 February 2012
Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proven. Applications of these results to constrained generalized pseudoinverse are included.
AMS Subject Classifications: 49J40; 65K05; 47H09.