Cartesian P-property and Its Applications to the Semidefinite Linear Complementarity Problem |
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Authors: | Xin Chen Houduo Qi |
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Affiliation: | (1) Department of Mechanical and Industrial Engineering, University of Illinois Urbana-Champaign 224 Mechanical Engineering Bldg, MC-244 1206 West Green Street, Urbana, IL 61801, USA;(2) School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1BJ, UK |
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Abstract: | 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]. This work is supported by the annual grant A2004/23 of University of Southampton. |
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Keywords: | Cartesian P-property SDLCP Globally unique solvability Merit functions Non-interior continuation method |
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