The column-sufficiency and row-sufficiency of the linear transformation on Hilbert spaces

• Published in: Journal of global optimization Vol. 49; no. 1; pp. 109 - 123
• Main Authors: Miao, Xin-He, Huang, Zheng-Hai
• Format: Journal Article
• Language: English
• Published: Boston Springer US 2011; Springer Nature B.V
• Subjects: Computer Science; Hilbert space; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Real Functions; Lorentz cone; Linear complementarity problem; Row-sufficiency; Jordan product; Column-sufficiency

Given a real Hilbert space H with a Jordan product and being the Lorentz cone, , and let T : H → H be a bounded linear transformation, the corresponding linear complementarity problem is denoted by LCP( T , Ω, q ). In this paper, we introduce the concepts of the column-sufficiency and row-sufficienc...