B0894
Title: Optimal design, Lagrangian and linear model theories: A fusion
Authors: Ben Torsney - Glasgow (United Kingdom) [presenting]
Abstract: We consider the problem of optimizing a criterion of several variables, subject to them satisfying several linear equality constraints. Lagrangian Theory requires that at an optimum all partial derivatives be exactly linear in a set of Lagrange Multipliers. It seems we can argue that the partial derivatives, viewed as response variables, must exactly satisfy a Linear Model with the Lagrange Multipliers as parameters. This then is a model without errors implying a fitted model with zero residuals. The residuals appear to play the role of directional derivatives in optimal design. Further, if all variables are nonnegative, we can exploit the multiplicative algorithm for finding optimal design weights.
