Characterization of the Cone and Applications in Banach Spaces. (26th October 2019)

• Record Type: Journal Article
• Authors: Kong, Dezhou; Liu, Lishan; Wu, Yonghong
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 14(2019)
• Page Start: 1703
• Page End: 1719
• Publication Date: 2019-10-26
• Subjects: Cone -- Banach spaces -- metric projection -- variational inequality -- complementarity problem; 41A65 -- 47H07 -- 06B30 -- 47J20 -- 47H10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1641115
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations of the metric projection onto cones and order intervals are obtained. As applications, the solvability and approximation results of solutions to nonlinear discontinuous variational inequality and complementarity problems are proved by partial ordering methods.