A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

Abstract

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.