On the Lipschitz continuity of the solution map in semidefinite linear complementarity problems

• 成果类型: Article
• 署名作者: Balaji, R; Parthasarathy, T; Raman, DS; Vetrivel, V
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras; University of Hyderabad; Indian Statistical Institute; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Madras
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1040.0134
• 发表日期: 2005
• 页码: 462-471
• 关键词: Monotonicity; matrices

摘要

In this paper, we investigate the Lipschitz continuity of the solution map in semidefinite linear complementarity problems. For a monotone linear transformation defined on the space of real symmetric n x n matrices, we show that the Lipschitz continuity of the solution map implies the globally uniquely solvable (GUS)-property. For Lyapunov transformations with the Q-property, we prove that the Lipschitz continuity of the solution map is equivalent to the strong monotonicity property. For the double-sided multiplicative transformations, we show that the Lipschitz continuity of the solution map implies the GUS-property.