Invited Discussion Paper Constrained Optimization of Experimental Design

. This is an attempt to discuss various approaches developed in experimental design when constraints are imposed. These constraints may be on the total cost of the experiment, the location of the supporting point, the value of auxiliary objective functions, and so on. The basic idea of the paper is that all 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 details, emphasizing ideas rather than technicalities. This is not intended as a literature review. The authors subjectively surely left many excellent papers behind.