@misc{Sagnol, author = {Sagnol, Guillaume}, title = {Network-related problems in Optimal Experimental Design and Second Order Cone Programming}, volume = {51}, number = {51}, issn = {1438-0064}, doi = {10.2478/v10127-012-0016-x}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14942}, pages = {161 -- 171}, abstract = {In the past few years several applications of optimal experimental designs have emerged to optimize the measurements in communication networks. The optimal design problems arising from this kind of applications share three interesting properties: (i) measurements are only available at a small number of locations of the network; (ii) each monitor can simultaneously measure several quantities, which can be modeled by ``multiresponse experiments"; (iii) the observation matrices depend on the topology of the network. In this paper, we give an overview of these experimental design problems and recall recent results for the computation of optimal designs by Second Order Cone Programming (SOCP). New results for the network-monitoring of a discrete time process are presented. In particular, we show that the optimal design problem for the monitoring of an AR1 process can be reduced to the standard form and we give experimental results.}, language = {en} } @misc{Sagnol, author = {Sagnol, Guillaume}, title = {A Class of Semidefinite Programs with rank-one solutions}, issn = {1438-0064}, doi = {10.1016/j.laa.2011.03.027}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14933}, abstract = {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.}, language = {en} }