<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Construction of constrained experimental designs on finite spaces for a modified E<italic>k</italic>-optimality criterion

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Construction of constrained experimental designs on finite spaces for a modified E-optimality criterion

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...

Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion

Published Online: Dec 31, 2020

Page range: 659 - 677

Received: May 23, 2020

Accepted: Oct 13, 2020

DOI: https://doi.org/10.34768/amcs-2020-0049

Keywords
constrained optimum experimental design, minimal sum of largest eigenvalues, generalized simplicial decomposition, optimal measurement selection

© 2020 Dariusz Uciński, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion

Published Online: Dec 31, 2020

Page range: 659 - 677

Received: May 23, 2020

Accepted: Oct 13, 2020

DOI: https://doi.org/10.34768/amcs-2020-0049

Keywordsconstrained optimum experimental design, minimal sum of largest eigenvalues, generalized simplicial decomposition, optimal measurement selection

© 2020 Dariusz Uciński, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
constrained optimum experimental design, minimal sum of largest eigenvalues, generalized simplicial decomposition, optimal measurement selection