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On Generalized Bolza Problem and Its Application to Dynamic Optimization

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  • Alexander D. Ioffe

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Abstract

We consider two classes of problems: unconstrained variational problems of Bolza type and optimal control problems with state constraints for systems governed by differential inclusions, both under fairly general assumptions, and prove necessary optimality conditions for both of them. The proofs using techniques of variational analysis are rather short, compared to the existing proofs, and the results seem to cover and extend the now available. The key step in the proof of the necessary conditions for the second problem is an equivalent reduction to one or a sequence of reasonably simple versions of the first.

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  • Alexander D. Ioffe, 2019. "On Generalized Bolza Problem and Its Application to Dynamic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 285-309, July.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:1:d:10.1007_s10957-019-01485-z
    DOI: 10.1007/s10957-019-01485-z
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    References listed on IDEAS

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    1. A. D. Ioffe, 1984. "Necessary Conditions in Nonsmooth Optimization," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 159-189, May.
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    Cited by:

    1. Nikolai Pavlovich Osmolovskii, 2020. "Necessary Second-Order Conditions for a Strong Local Minimum in a Problem with Endpoint and Control Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 1-16, April.

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