Network-related problems in Optimal experimental design and second order Cone programming

Abstract

In the past few years several applications of optimal experimental designs have
emerged to optimize the measurements of certain quantities 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.