ON STEIN TRANSFORMATION IN SEMIDEFINITE LINEAR COMPLEMENTARITY PROBLEMS
- Authors
- 송윤정; Seon Ho Shin
- Issue Date
- Jan-2014
- Publisher
- 한국전산응용수학회
- Keywords
- Stein Transformation; Semidenite Linear Com- plementarity Problems (SDLCP); GUS-property; P′ 2-property
- Citation
- Journal of Applied Mathematics and Informatics, v.32, no.1, pp.285 - 295
- Journal Title
- Journal of Applied Mathematics and Informatics
- Volume
- 32
- Number
- 1
- Start Page
- 285
- End Page
- 295
- URI
- http://scholarworks.bwise.kr/ssu/handle/2018.sw.ssu/10311
- ISSN
- 1598-5857
- Abstract
- In the setting of semidenite linear complementarity problems on Sn, we focus on the Stein Transformation SA(X) := X −AXAT , and show that SA is (strictly) monotone if and only if r(UAUT ◦UAUT ) (< ) ≤ 1 for all orthogonal matrices U where ◦is the Hadamard product and r is the real numerical radius. In particular, we show that if (A) < 1 and r(UAUT ◦UAUT ) ≤ 1, then SDLCP(SAQ) has a unique solution for all Q ∈ Sn. In an attempt to characterize the GUS-property of a nonmonotone SA, we give an instance of a nonnormal 2 × 2 matrix A such that SDLCP(SAQ) has a unique solution for Q either a diagonal or a symmetric positive or negative semidenite matrix. We show that this particular SA has the P′ 2-property.
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