Constrained Optimization of Experimental Design

This is an attempt to discuss various approaches developed in experimental design when some constraints are imposed. The constraints may be on the total cost of the experiment, the location of the supporting point, the value of the auxiliary objective functions, and so on. The basic idea of the paper is that corresponding optimization problems can be imbedded in the convex theory of experimental design. Part 1 is concerned with the properties of optimal designs, while Part 2 is devoted mainly to numerical methods. We have tried to avoid detail emphasizing ideas rather than technicalities. This is not intended as a literature review. The authors subjectively, surely left many excellent papers behind. 1 Equivalence Theorems 1.1 Introduction Experimental design problems considered in this paper are basically related to the standard linear regression model: y ij = j(x i ; `) + ffl ij ; (1) i = 1; : : : ; n; j = 1; : : : ; r i ; Σr i = N; j(x; `) = ` T f(x) where `fflR m are ...