A Class of Semidefinite Programs with rank-one solutions
Please always quote using this URN: urn:nbn:de:0297-zib-14933
- We show that a class of semidefinite programs (SDP) admits a solution that is a positive semidefinite matrix of rank at most $r$, where $r$ is the rank of the matrix involved in the objective function of the SDP. The optimization problems of this class are semidefinite packing problems, which are the SDP analogs to vector packing problems. Of particular interest is the case in which our result guarantees the existence of a solution of rank one: we show that the computation of this solution actually reduces to a Second Order Cone Program (SOCP). We point out an application in statistics, in the optimal design of experiments.
Author: | Guillaume Sagnol |
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Document Type: | ZIB-Report |
Tag: | Low-rank solutions; Multiresponse experiments; Optimal Experimental Design; SDP; SOCP; Semidefinite Packing Problem; rank 1-solution |
MSC-Classification: | 62-XX STATISTICS |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING | |
CCS-Classification: | G. Mathematics of Computing |
Date of first Publication: | 2012/03/27 |
Series (Serial Number): | ZIB-Report (11-51) |
ISSN: | 1438-0064 |
Published in: | Appeared in: Linear Algebra and its Applications 435 (2011) pp. 1446-1463 |
DOI: | https://doi.org/10.1016/j.laa.2011.03.027 |