A projected Newton method in a Cartesian product of balls |
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Authors: | M. Gawande J. C. Dunn |
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Affiliation: | (1) Department of Mathematics, North Carolina State University, Raleigh, North Carolina;(2) Present address: AT&T Bell Laboratories, Holmdel, New Jersey |
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Abstract: | We formulate a locally superlinearly convergent projected Newton method for constrained minimization in a Cartesian product of balls. For discrete-time,N-stage, input-constrained optimal control problems with Bolza objective functions, we then show how the required scaled tangential component of the objective function gradient can be approximated efficiently with a differential dynamic programming scheme; the computational cost and the storage requirements for the resulting modified projected Newton algorithm increase linearly with the number of stages. In calculations performed for a specific control problem with 10 stages, the modified projected Newton algorithm is shown to be one to two orders of magnitude more efficient than a standard unscaled projected gradient method.This work was supported by the National Science Foundation, Grant No. DMS-85-03746. |
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Keywords: | Constrained minimization projected Newton method optimal control differential dynamic programming |
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