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.

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Author:Guillaume Sagnol
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