  We present a systematic approach to the optimal placement of finitely many
sensors in order to infer a finite-dimensional parameter from point evaluations
of the solution of an associated parameter-dependent elliptic PDE. The quality
of the corresponding least squares estimator is quantified by properties of the
asymptotic covariance matrix depending on the distribution of the measurement
sensors. We formulate a design problem where we minimize functionals related to
the size of the corresponding confidence regions with respect to the position
and number of pointwise measurements. The measurement setup is modeled by a
positive Borel measure on the spatial experimental domain resulting in a convex
optimization problem. For the algorithmic solution a class of accelerated
conditional gradient methods in measure space is derived, which exploits the
structural properties of the design problem to ensure convergence towards
sparse solutions. Convergence properties are presented and the presented
results are illustrated by numerical experiments.
