An optimal design of experiment is a rule of selecting the measurements which provide the maximum possible amount of information about the unknown parameters of the underlying statistical model. From the mathematical point of view, the construction of an optimal "approximate" design is a special problem of convex optimization on the unit n-simplex, a relaxation of the problem of constructing an optimal "exact" experimental design. In the talk we will describe two classic algorithms for constructing optimal approximate designs: Fedorov-Wynn steepest descent algorithm and Titterington-Torsney multiplicative algorithm. We also give examples of design problems that can be efficiently solved using the methods of mathematical programming, ranging from linear programming to semidefinite programming.
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