Abstract
The properties of combined multiplier and penalty function methods are investigated using a second-order expansion and results known for the Riccati equation. It is shown that the lower bound of the values of the penalty constant necessary to obtain a minimum is given by a certain Riccati equation. The convergence rate of a common updating rule for the multipliers is shown to be linear.
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Communicated by M. R. Hestenes
This work has been supported by the Swedish Institute of Applied Mathematics.
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Glad, S.T. A combination of penalty function and multiplier methods for solving optimal control problems. J Optim Theory Appl 28, 303–329 (1979). https://doi.org/10.1007/BF00933377
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DOI: https://doi.org/10.1007/BF00933377