Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization

• Published in: Fixed point theory and algorithms for sciences and engineering Vol. 2012; no. 1; pp. 1 - 24
• Main Authors: Zeng, L C, Wong, M M, Yao, J C
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 27.02.2012; Springer Nature B.V; BioMed Central Ltd
• Subjects: Algorithms; Analysis; Applications of Mathematics; Constraints; Convergence; Differential Geometry; Inequalities; Mapping; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Networks; Optimization; Resource allocation; Topology; relaxed hybrid steepest-descent method; fixed point; nonexpansive mapping; variational inequality; strong convergence; triple-hierarchical constrained optimization; monotone operator
• ISSN: 1687-1812; 1687-1820; 1687-1812; 2730-5422
• DOI: 10.1186/1687-1812-2012-29

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.