Impulse Control in Operations Research: Necessary Optimality Conditions, Sufficiency and Existence (replaced by CentER DP 2011-133)
AbstractThis paper considers a class of optimal control problems that allows jumps in the state variable. We present the necessary optimality conditions of the Impulse Control Maximum Principle based on the current value formulation. By reviewing the existing impulse control models in the literature, we point out that meaningful problems do not satisfy the sufficiency conditions. In particular, such problems either have a concave cost function, contain a fixed cost, or have a control-state interaction, which have in common that they each violate the concavity property of the underlying model. The implication is that the corresponding problem in principle has multiple solutions that satisfy the necessary optimality conditions. Moreover, we argue that problems with fixed cost do not satisfy the conditions under which the necessary optimality conditions can be applied. However, we design a transformation, which ensures that the application of the Impulse Control Maximum Principle still provides the optimal solution. Finally, we show for the first time that for some existing models in the literature no optimal solution exists.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-052.
Date of creation: 2011
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Impulse Control Maximum Principle; Optimal Control; discrete continuous system; state-jumps; present value formulation;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D90 - Microeconomics - - Intertemporal Choice - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-05-30 (All new papers)
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- Chahim, M. & Brekelmans, R.C.M. & Hertog, D. den & Kort, P.M., 2011. "An Impulse Control Approach to Dike Height Optimization (Replaced by CentER DP 2012-079)," Discussion Paper 2011-097, Tilburg University, Center for Economic Research.
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