Numerical Algorithms for Deterministic Impulse Control Models with Applications
AbstractAbstract: In this paper we describe three different algorithms, from which two (as far as we know) are new in the literature. We take both the size of the jump as the jump times as decision variables. The first (new) algorithm considers an Impulse Control problem as a (multipoint) Boundary Value Problem and uses a continuation technique to solve it. The second (new) approach is the continuation algorithm that requires the canonical system to be solved explicitly. This reduces the infinite dimensional problem to a finite dimensional system of, in general, nonlinear equations, without discretizing the problem. Finally, we present a gradient algorithm, where we reformulate the problem as a finite dimensional problem, which can be solved using some standard optimization techniques. As an application we solve a forest management problem and a dike heightening problem. We numerically compare the efficiency of our methods to other approaches, such as dynamic programming, backward algorithm and value function approach.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-081.
Date of creation: 2012
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Impulse ControlMaximum Principle; Optimal Control; BVP; gradient method; continuation;
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
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- Erdlenbruch, Katrin & Jean-Marie, Alain & Moreaux, Michel & Tidball, Mabel, 2010.
"Optimality of Impulse Harvesting Policies,"
IDEI Working Papers
603, Institut d'Économie Industrielle (IDEI), Toulouse.
- Erdlenbruch, Katrin & Jean-Marie, Alain & Moreaux, Michel & Tidball, Mabel, 2010. "Optimality of Impulse Harvesting Policies," TSE Working Papers 09-150, Toulouse School of Economics (TSE).
- Katrin Erdlenbruch & Alain Jean-Marie & Michel MOREAUX & Mabel Tidball, 2010. "Optimality of Impulse Harvesting Policies," LERNA Working Papers 10.09.315, LERNA, University of Toulouse.
- Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2010. "Optimality of Impulse Harvesting Policies," Working Papers hal-00864187, HAL.
- Chahim, Mohammed & Hartl, Richard F. & Kort, Peter M., 2012. "A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 18-26.
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