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

Cartesian P-property and its applications to the semidefinite linear complementarity problem
Cartesian P-property and its applications to the semidefinite linear complementarity problem
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].
Cartesian P-property, SDLCP, globally unique solvability, merit functions, non-interior continuation method
0025-5610
177-201
Chen, Xin
927cf7ef-386c-42b5-aac4-c35836675619
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Chen, Xin
927cf7ef-386c-42b5-aac4-c35836675619
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85

Chen, Xin and Qi, Houduo (2006) Cartesian P-property and its applications to the semidefinite linear complementarity problem. Mathematical Programming, 106 (1), 177-201. (doi:10.1007/s10107-005-0601-8).

Record type: Article

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].

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More information

Published date: March 2006
Keywords: Cartesian P-property, SDLCP, globally unique solvability, merit functions, non-interior continuation method
Organisations: Operational Research

Identifiers

Local EPrints ID: 38474
URI: https://eprints.soton.ac.uk/id/eprint/38474
ISSN: 0025-5610
PURE UUID: 43dff292-b030-4075-b1dd-6d90f3c954c2
ORCID for Houduo Qi: ORCID iD orcid.org/0000-0003-3481-4814

Catalogue record

Date deposited: 23 Mar 2010
Last modified: 06 Oct 2018 00:35

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