Abstract
Using a penalty function method, a Lagrange multiplier theorem in dual Banach spaces is proved. This theorem is applied to the optimal control of linear, autonomous time-delay systems with function space equality end condition and pointwise control restrictions. Under an additional regularity condition, the resulting Lagrange multiplier can be identified with an element ofL ∞.
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Communicated by A. V. Balakrishnan
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Colonius, F. A penalty function proof of a Lagrange multiplier theorem with application to linear delay systems. Appl Math Optim 7, 309–334 (1981). https://doi.org/10.1007/BF01442124
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DOI: https://doi.org/10.1007/BF01442124