On the bilinearity rank of a proper cone and Lyapunov-like transformations

• 成果类型: Article
• 署名作者: Gowda, M. Seetharama; Tao, Jiyuan
• 署名单位: University System of Maryland; University of Maryland Baltimore County; Loyola University Maryland
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0715-3
• 发表日期: 2014
• 页码: 155-170
• 关键词: symmetric cones

摘要

A real square matrix is a bilinear complementarity relation on a proper cone in if where is the dual of . The bilinearity rank of is the dimension of the linear space of all bilinear complementarity relations on . In this article, we continue the study initiated by Rudolf et al. (Math Prog Ser B 129:5-31, 2011). We show that bilinear complementarity relations are related to Lyapunov-like transformations that appear in dynamical systems and in complementarity theory and further show that the bilinearity rank of is the dimension of the Lie algebra of the automorphism group of . In addition, we correct a result of Rudolf et al., compute the bilinearity ranks of symmetric and completely positive cones, and state some Schur-type results for Lyapunov-like transformations.