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No such thing as a perfect hammer: comparing different objective function specifications for optimal control

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  • D. Blueschke

    () (Alpen-Adria-Universität Klagenfurt)

  • I. Savin

    (Karlsruhe Institute of Technology
    Université de Strasbourg
    Friedrich Schiller University of Jena
    Ural Federal University)

Abstract

Linear-quadratic (LQ) optimization is a fairly standard technique in the optimal control framework. LQ is very well researched, and there are many extensions for more sophisticated scenarios like nonlinear models. Conventionally, the quadratic objective function is taken as a prerequisite for calculating derivative-based solutions of optimal control problems. However, it is not clear whether this framework is as universal as it is considered to be. In particular, we address the question whether the objective function specification and the corresponding penalties applied are well suited in case of a large exogenous shock an economy can experience because of, e.g., the European debt crisis. While one can still efficiently minimize quadratic deviations around policy targets, the economy itself has to go through a period of turbulence with economic indicators, such as unemployment, inflation or public debt, changing considerably over time. We test four alternative designs of the objective function: a least median of squares based approach, absolute deviations, cubic and quartic objective functions. The analysis is performed based on a small-scale model of the Austrian economy and illustrates a certain trade-off between quickly finding an optimal solution using the LQ technique (reaching defined policy targets) and accounting for alternative objectives, such as limiting volatility in economic performance. As an implication, we argue in favor of the considerably more flexible optimization technique based on heuristic methods (such as Differential Evolution), which allows one to minimize various loss function specifications, but also takes additional constraints into account.

Suggested Citation

  • D. Blueschke & I. Savin, 2017. "No such thing as a perfect hammer: comparing different objective function specifications for optimal control," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 377-392, June.
  • Handle: RePEc:spr:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-016-0446-7
    DOI: 10.1007/s10100-016-0446-7
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    References listed on IDEAS

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    5. Dimitri Blueschke & Viktoria Blüschke-Nikolaeva & Ivan Savin, 2015. "Slow and steady wins the race: approximating Nash equilibria in nonlinear quadratic tracking games," Jena Economic Research Papers 2015-011, Friedrich-Schiller-University Jena.
    6. Blueschke, D. & Blueschke-Nikolaeva, V. & Savin, I., 2013. "New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 821-837.
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    Cited by:

    1. D. Blueschke & I. Savin & V. Blueschke-Nikolaeva, 2020. "An Evolutionary Approach to Passive Learning in Optimal Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(3), pages 659-673, October.

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    More about this item

    Keywords

    Differential evolution; Nonlinear optimization; Optimal control; Least median of squares;
    All these keywords.

    JEL classification:

    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination
    • E63 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Comparative or Joint Analysis of Fiscal and Monetary Policy; Stabilization; Treasury Policy

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