The theory of optimal experimental design plays a central role in statistics. It studies how to best select experiments in order to estimate a set of unknown parameters. A common approach is to distribute the experimental effort so as to minimize a scalar function measuring the size of the confidence ellipsoids of an estimator for the unknown parameter. This leads to a convex optimization problem involving a spectral function which is applied to the information matrix of the experiments.
While new applications of experimental design arise, in particular for the monitoring of large communication networks, there is a need for algorithms that can solve very large instances of this kind of optimization problems. In this talk we shall review the classical algorithms, present recent developments and explore new directions to compute optimal designs.
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