Abstract
The multiple-shooting method for the solution of boundary-value problems is a modified Newton method for the solution of an equationℱ(x) = 0, whereℱ is a special function which is differentiable in general, but may occasionally have discontinuities at some points which have to be passed during the iteration process. This is the case especially in optimal control problems and it is a severe handicap for the convergence of the Newton method which can be essentially reduced when replacingℱ by a series of smooth functionsℱ i dependent on the iteration process.
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Communicated by J. Stoer
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Kiehl, M. Smoothing the function of the multiple-shooting equation. Appl Math Optim 24, 171–181 (1991). https://doi.org/10.1007/BF01447740
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DOI: https://doi.org/10.1007/BF01447740