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Number 4 - December 2020
Volume 30 - 2020
Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion
Dariusz Uciński
Abstract
A simple computational algorithm is proposed for minimizing sums of largest eigenvalues of the matrix inverse over the
set of all convex combinations of a finite number of nonnegative definite matrices subject to additional box constraints on
the weights of those combinations. Such problems arise when experimental designs aiming at minimizing sums of largest
asymptotic variances of the least-squares estimators are sought and the design region consists of finitely many support
points, subject to the additional constraints that the corresponding design weights are to remain within certain limits. The
underlying idea is to apply the method of outer approximations for solving the associated convex semi-infinite programming
problem, which reduces to solving a sequence of finite min-max problems. A key novelty here is that solutions to the latter
are found using generalized simplicial decomposition, which is a recent extension of the classical simplicial decomposition
to nondifferentiable optimization. Thereby, the dimensionality of the design problem is drastically reduced. The use of
the algorithm is illustrated by an example involving optimal sensor node activation in a large sensor network collecting
measurements for parameter estimation of a spatiotemporal process.
Keywords
constrained optimum experimental design, minimal sum of largest eigenvalues, generalized simplicial decomposition, optimal measurement selection