Direct gradient approaches for optimizing smooth, nonsmoooth and stochastic dynamic economic systems

Sandblom, C.-L. & Uryas'ev, S.P. (1990). Direct gradient approaches for optimizing smooth, nonsmoooth and stochastic dynamic economic systems. In: Dynamic Modelling and Control of National Economies 1989. Eds. Christodoulakis, N.M., pp. 139-143 Oxford, UK: Pergamon Press. ISBN 978-0-08-037538-0 10.1016/B978-0-08-037538-0.50027-7.

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Abstract

There are different approaches to optimize a deterministic dynamic economic system, expressed in structural or reduced form. In this paper we explore the direct method where the model equations are used to solve for the endogenous variables, which are then eliminated from the criterion functions, resulting in an optimization problem involving only the control variables. This problem is mostly of much lower dimension than the original one, and it is shown how the gradients of the criterion function can be easily calculated. For the linear-quadratic case we show how the optimality conditions can be expressed so that the matrix Riccati equation results; for this problem approaches are therefore equivalent. However, the direct gradient approach is of considerable more generality, allowing for instance nonlinear model equations which may include stochastic coefficients and/or general nonsmooth criterion functions. In this paper we explore these more general situations. Quadratic and minimax type objective functions are used and the usefulness of the approach is discussed.

Item Type:	Book Section
Additional Information:	Selected Papers from the 6th IFAC Symposium, Edinburgh, UK, 27–29 June 1989
Research Programs:	System and Decision Sciences - Core (SDS)
Depositing User:	Romeo Molina
Date Deposited:	18 Apr 2016 08:52
Last Modified:	27 Aug 2021 17:26
URI:	https://pure.iiasa.ac.at/12745

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