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Statistica Sinica 7(1997), 739-753



Adalbert Wilhelm

Universität Augsburg

Abstract: Essentially two classes of iterative procedures have been proposed in the literature to solve optimal design problems in linear regression: exchange algorithms devoted to the construction of optimal exact designs in a finite design space and methods from convex programming yielding optimal moment matrices only. By simultaneously taking weights and support points as variables the design problem represents a nonconcave, not necessarily differentiable, but Lipschitz continuous maximization problem. We, therefore, adapt bundle trust methods from nondifferentiable optimization to the design problem and show their numerical behaviour. Explicit efficiency bounds for the numerical solutions can be given in the case of a regression range with finitely many elements.

Key words and phrases: Approximate designs, bundle trust methods, nondifferentiability, pth matrix means, support points and weig hts.

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