Z-transformations on proper and symmetric cones - Z-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
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0159-8
• 发表日期: 2009
• 页码: 195-221
• 关键词: p-properties; COMPLEMENTARITY; lyapunov; THEOREM; stein; forms

摘要

Motivated by the similarities between the properties of Z-matrices on R-+(n) and Lyapunov and Stein transformations on the semidefinite cone S-+(n), we introduce and study Z-transformations on proper cones. We show that many properties of Z-matrices extend to Z-transformations. We describe the diagonal stability of such a transformation on a symmetric cone by means of quadratic representations. Finally, we study the equivalence of Q and P properties of Z-transformations on symmetric cones. In particular, we prove such an equivalence on the Lorentz cone.