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A non-classical class of variational problems

Cruz, P., Torres, A.F., Delfim, F.M. and Zinober, A.S.I. (2010) A non-classical class of variational problems. International Journal of Mathematical Modelling and Numerical Optimisation, 1 (3). pp. 227-236. ISSN 2040-3607

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Abstract

We study a new non-classical class of variational problems that is motivated by some recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the calculus of variations (CoV) or optimal control. However, the state value at the final fixed time, y(T), is a priori unknown and the integrand is a function of the unknown y(T). This is a non-standard CoV problem. In this paper we apply the new costate boundary conditions p(T) in the formulation of the CoV problem. We solve a sample example in this problem class using the numerical shooting method to solve the resulting TPBVP, and incorporate the free y(T) as an additional unknown. Essentially the same results are obtained using symbolic algebra software.

Item Type: Article
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mrs Megan Hobbs
Date Deposited: 22 Mar 2010 11:58
Last Modified: 07 Jun 2010 11:10
Published Version: http://dx.doi.org/10.1504/IJMMNO.2010.031750
Status: Published
Publisher: Inderscience Publishers
Identification Number: 10.1504/IJMMNO.2010.031750
URI: http://eprints.whiterose.ac.uk/id/eprint/10643

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