### On construction of constrained optimum designs

Ucinski, D *(Zielona Gora)*

Friday 15 August 2008, 16:30-17:00

Seminar Room 1, Newton Institute

#### Abstract

A simple computational algorithm is proposed for maximization of a concave function 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 commonly arise when optimum experimental designs are sought over a design region consisting 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 a simplicial decomposition algorithm in which the restricted master problem reduces to an uncomplicated weight optimization one. Global convergence to the optimal solution is established and the use of the algorithm is illustrated by examples involving D-optimal design of measurement effort for parameter estimation of a multiresponse chemical kinetics process, as well as sensor selection in a large-scale monitoring network for parameter estimation of a process described by a two-dimensional diffusion equation. Parallelization of the procedure and extensions to general continuous designs are also discussed.

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