Abstract
In this paper, sequential gradient-restoration algorithms for optimal control problems are considered, and attention is focused on the restoration phase. It is shown that the Lagrange multipliers associated with the restoration phase not only solve the auxiliary minimization problem of the restoration phase, but are also endowed with a supplementary optimality property: they minimize a special functional, quadratic in the multipliers, subject to the multiplier differential equations and boundary conditions, for given state, control, and parameter.
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Dedicated to L. Cesari
This work was supported by a grant of the National Science Foundation.
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Miele, A., Wang, T. Supplementary optimality properties of the restoration phase of sequential gradient-restoration algorithms for optimal control problems. J Optim Theory Appl 41, 169–184 (1983). https://doi.org/10.1007/BF00934442
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DOI: https://doi.org/10.1007/BF00934442