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Title: A non-classical class of variational problems
Author: João Pedro Cruz
Delfim Torres
Alan S. I. Zinober
Keywords: Non-linear revenue problems
Transversality conditions
Calculus of variations
Shooting method
Optimal control
Issue Date: 2010
Publisher: Inderscience
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.
Peer review: yes
ISSN: 2040-3607
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Appears in Collections:MAT - Artigos

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