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Pitfalls in parameter estimation for delay differential equations. (English) Zbl 0867.65032
The problem of estimating unknown parameters in delay differential equations (DDEs) is investigated. This problem can be resolved by minimizing a least squares objective function. The smoothness of the objective function is studied. As a result it is shown that the objective function commonly used is not necessarily smooth. The derivative discontinuity tracking theory for DDEs is used to analyze how jumps can arise in the derivative of a natural objective function. These jumps are not expected to occur in parameter estimation problems for ordinary differential equations.
Reviewer: T.E.Simos (Athens)

MSC:
65K10 Numerical optimization and variational techniques
65L05 Numerical methods for initial value problems
34K35 Control problems for functional-differential equations
34A55 Inverse problems involving ordinary differential equations
34K05 General theory of functional-differential equations
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