On generalized Bolza problem and its application to dynamic optimization. (English) Zbl 1420.49027
Summary: 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.
MSC:
| 49K21 | Optimality conditions for problems involving relations other than differential equations |
| 49J53 | Set-valued and variational analysis |
| 49J52 | Nonsmooth analysis |
| 58C06 | Set-valued and function-space-valued mappings on manifolds |
Keywords:
optimal control; differential inclusion; maximum principle; variational analysis; subdifferential calculusReferences:
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