Parthasarathy, T. ; Sampangi Raman, D. ; Sriparna, B. (2002) Relationship between strong monotonicity property, P2-property, and the GUS-property in semidefinite linear complementarity problems Mathematics of Operations Research, 27 (2). pp. 326-331. ISSN 0364-765X
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Official URL: http://mor.journal.informs.org/content/27/2/326.sh...
Related URL: http://dx.doi.org/10.1287/moor.27.2.326.319
Abstract
In a recent paper on semidefinite linear complementarity problems, Gowda and Song (2000) introduced and studied the P-property, P2-property, GUS-property, and strong monotonicity property for linear transformation L: Sn → Sn, where Sn is the space of all symmetric and real n × n matrices. In an attempt to characterize the P2-property, they raised the following two questions: (i) Does the strong monotonicity imply the P2-property? (ii) Does the GUS-property imply the P2-property? In this paper, we show that the strong monotonicity property implies the P2-property for any linear transformation and describe an equivalence between these two properties for Lyapunov and other transformations. We show by means of an example that the GUS-property need not imply the P2-property, even for Lyapunov transformations.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Informs. |
| Keywords: | Semidefinite Linear Complementarity Problem; Positive Semidefinite Matrix; Lyapunov Transformation; GUS-property; Strong Monotonicity Property; P2-property |
| ID Code: | 90950 |
| Deposited On: | 15 May 2012 10:00 |
| Last Modified: | 15 May 2012 10:00 |
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