Multiplication Algorithms for Approximate Optimal Distributions with Cost Constraints

Abstract

In this paper, we study the D- and A-optimal assignment problems for regression models with experimental cost constraints. To solve these two problems, we propose two multiplicative algorithms for obtaining optimal designs and establishing extended D-optimal (ED-optimal) and A-optimal (EA-optimal) criteria. In addition, we give proof of the convergence of the ED-optimal algorithm and draw conjectures about some properties of the EA-optimal algorithm. Compared with the classical D- and A-optimal algorithms, the ED- and EA-optimal algorithms consider not only the accuracy of parameter estimation, but also the experimental cost constraint. The proposed methods work well in the digital example.

Keywords

• D-optimal
• A-optimal
• experimental design
• Kuhn–Tucker method
• experimental cost