Numerical Algorithms for Deterministic Impulse Control Models with Applications
CentER Discussion Paper Series No. 2012-081
22 Pages Posted: 20 Oct 2012
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: Suggested Citation