Name
Title | ||
|---|---|---|
Cartesian P-property and Its Applications to the Semidefinite Linear Complementarity Problem |
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]. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s10107-005-0601-8 | Math. Program. |
Keywords | Field | DocType |
input data,corresponding p-properties,numerical approach,cartesian p-property,linear transformation,non-interior continuation method,merit functions,semidefinite linear complementarity problem,general sdlcps,globally unique solvability,sdlcp,newton direction,important theoretical issue,cartesian p -property,monotone sdlcps,symmetric matrices,linear complementarity problem | Mathematical optimization,Symmetric matrix,Stationary point,Linear map,Linear complementarity problem,Numerical analysis,Iterated function,Mathematics,Monotone polygon,Cartesian coordinate system | Journal |
Volume | Issue | ISSN |
106 | 1 | 1436-4646 |
Citations | PageRank | References |
17 | 0.74 | 23 |
Authors | ||
2 | ||