Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bray, J. (1972) ‘Some Considerations in the Practice of Economic Management’, PREM Discussion Paper no. 2.
Bray, J. (1975), ‘Optimal Control of a Noisy Economy with the U.K. as an Example’, J. R. Statist. Soc., series A, vol. 138, part 3.
Broyden, C. (1967), ‘Quasi-Newton Methods and their Application to Function Minimisation’, Math. of Comp., v. 21, pp. 368–81.
Canon, M. D., Cullum, C. D., and Polak, E. (1970), Theory of Optimal Control and Mathematical Programming, (McGraw-Hill, New York).
Davidon, W. C. (1968) ‘Variance Algorithm for Minimization’, Comp. J., v. 10, pp. 406–10.
Fiacco, A.V., and McCormick, G. P. (1968), Nonlinear Programming: Sequential Unconstrained Minimization Techniques (John Wiley, New York).
Friedman, B. (1972), ‘Optimal Economic Stabilization Policy: An Extended Framework’, J. Polit. Econ. vol. Lxxx, pp. 1002–22.
Frisch, R. (1972), ‘Cooperation between Politicians and Econometricians on the Formalization of Political Preferences’, University of Oslo, Institute of Economics Reprint Series No. 90.
Holly, S. et al. (1977), ‘Control Exercises with a Small Linear Model of the U.K. Economy’ (Chapter 8 of this volume).
Livesey, D. (1973), ‘Can Macro-Economic Planning Problems Ever be Treated as a Quadratic Regulator Problem? IEE Conference Publications, vol. 101, pp. 1–14.
Livesey, D. (1976), ‘Feasible Directions in Economic Policy’, presented at the European Meeting of the Econometric Society, Helsinki, 1976.
Luenberger, D. (1969), Optimization by Vector Space Methods (John Wiley, New York).
Murtagh, B. A., and Sargent, R. W. H. (1969), ‘A Constrained Minimization Method with Quadratic Convergence’, in R. Fletcher (ed.), Optimization (Academic Press, New York and London).
Murtagh, B. A., and Sargent, R. W. H. (1970), ‘Computational Experience with Quadratically Convergent Minimization Methods’, Comp. J., vol. 13, pp. 185–94.
Polak, E. (1971), Computational Methods in Optimization (Academic Press, New York and London).
Rustem, B. (1978), ‘Projection Methods in Constrained Optimization’, PhD dissertation University of London.
Rustem, B., Velupillai, K., and Westcott, J. H. (1976), ‘A Method for Respecifying the Weighting Matrix of a Quadratic Criterion Function’, PREM Discussion Paper no. 15.
Westcott, J. H., Holly, S., Rustem, B., and Zarrop, M. (1976), ‘Control Theory in the Formulation of Economic Policy’, Submission to the Committee of Inquiry on Policy Optimisation.
Editor information
Editors and Affiliations
Copyright information
© 1979 B. Rüstem, J. H. Westcott, M. B. Zarrop, S. Holly and R. Becker
About this chapter
Cite this chapter
Rüstem, B., Westcott, J.H., Zarrop, M.B., Holly, S., Becker, R. (1979). Iterative Respecification of the Quadratic Objective Function. In: Holly, S., Rüstem, B., Zarrop, M.B. (eds) Optimal Control for Econometric Models. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-16092-1_6
Download citation
DOI: https://doi.org/10.1007/978-1-349-16092-1_6
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-16094-5
Online ISBN: 978-1-349-16092-1
eBook Packages: Palgrave Economics & Finance CollectionEconomics and Finance (R0)