Cartesian P-property and its applications to the semidefinite linear complementarity problem

• 成果类型: Article
• 署名作者: Chen, X; Qi, HD
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Southampton
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0601-8
• 发表日期: 2006
• 页码: 177-201
• 关键词: nonlinear complementarity; continuation methods; search directions; merit function; MONOTONICITY

摘要

We introduce a Cartesian P-property for linear transformations between the space of symmetric matrices and present its applications to the semidefinite linear complementarity problem (SDLCP). With this Cartesian P-property, we show that the SDLCP has GUS-property (i.e., globally unique solvability), and the solution map of the SDLCP is locally Lipschitzian with respect to input data. Our Cartesian P-property strengthens the corresponding P-properties of Gowda and Song [15] and allows us to extend several numerical approaches for monotone SDLCPs to solve more general SDLCPs, namely SDLCPs with the Cartesian P-property. In particular, we address important theoretical issues encountered in those numerical approaches, such as issues related to the stationary points in the merit function approach, and the existence of Newton directions and boundedness of iterates in the non-interior continuation method of Chen and Tseng [6].