Approximate D-optimal Experimental Design with Simultaneous Size and Cost Constraints

TL;DR

This paper develops a new method for constructing approximate D-optimal experimental designs that simultaneously consider size and cost constraints, providing theoretical foundations and a practical algorithm.

Contribution

It formulates an equivalence theorem and introduces a simple, convergent barycentric algorithm for size-and-cost constrained D-optimal design construction.

Findings

Established an equivalence theorem for constrained D-optimality

Proposed a monotonic barycentric algorithm for design computation

Demonstrated the effectiveness of the method through numerical examples

Abstract

Consider an experiment with a finite set of design points representing permissible trial conditions. Suppose that each trial is associated with a cost that depends on the selected design point. In this paper, we study the problem of constructing an approximate D-optimal experimental design with simultaneous restrictions on the size and on the total cost. For the problem of size-and-cost constrained D-optimality, we formulate an equivalence theorem and rules for the removal of redundant design points. We also propose a simple monotonically convergent "barycentric" algorithm that allows us to numerically compute a size-and-cost constrained approximate D-optimal design.