Iterative Respecification of the Quadratic Objective Function

A fundamental problem in the optimisation of policy decisions is the specification of a suitable objective function. It has been argued by Rustem, Velupillai and Westcott (1976) and Westcott, Holly, Rustem and Zarrop (1976) that quadratic functions penalising the weighted deviation of the computed trajectories from their desired values form an acceptable class of objective functions. An iterative method for specifying the weighting matrices of such quadratic functions has been reported by Rustem, Velupillai and Westcott (1976). The method is not concerned with a ‘best’ set of weights independent of the ‘best’ desired path; rather a politically acceptable path, optimally generated, is the main aim. This paper discusses the numerical considerations arising from the actual implementation of the algorithm described by Rustem, Velupillai and Westcott (1976). Basic concepts and the method are introduced in Sections 2 and 3 using formal mathematical definitions parallel to an intuitive approach to the underlying problem. Section 4 describes the computational aspects of the implementation of the algorithm and Section 5 illustrates the method giving numerical examples.