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On Generalized Bolza Problem and Its Application to Dynamic Optimization

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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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Notes

  1. Actually, it will be sufficient to assume that L(t, x(t), y(t)) is measurable if so are x(t) and y(t)

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Acknowledgements

I wish to express my gratitude to the anonymous referee for helpful remarks.

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  1. Department of Mathematics, Technion, 32000, Haifa, Israel

    Alexander D. Ioffe

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  1. Alexander D. Ioffe
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Correspondence to Alexander D. Ioffe.

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Ioffe, A.D. On Generalized Bolza Problem and Its Application to Dynamic Optimization. J Optim Theory Appl 182, 285–309 (2019). https://doi.org/10.1007/s10957-019-01485-z

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