Numerical Algorithms for Deterministic Impulse Control Models with Applications

CentER Discussion Paper Series No. 2012-081

22 Pages Posted: 20 Oct 2012

See all articles by Dieter Grass

Dieter Grass

affiliation not provided to SSRN

Mohammed Chahim

TNO Netherlands Organisation for Applied Scientific Research

Date Written: October 19, 2012

Abstract

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.

Keywords: Impulse Control, Maximum Principle, Optimal Control, BVP, Gradient Method

JEL Classification: C61, D90, O32, O33

Suggested Citation

Grass, Dieter and Chahim, Mohammed, Numerical Algorithms for Deterministic Impulse Control Models with Applications (October 19, 2012). CentER Discussion Paper Series No. 2012-081, Available at SSRN: https://ssrn.com/abstract=2164243 or http://dx.doi.org/10.2139/ssrn.2164243

Dieter Grass

affiliation not provided to SSRN ( email )

Mohammed Chahim (Contact Author)

TNO Netherlands Organisation for Applied Scientific Research ( email )

Delft
Netherlands

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