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.CEOCFCTFEDER/POCI 201
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