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First and second order sufficient conditions for optimal control and the calculus of variations. (English) Zbl 0558.49006
The author gives very elegant and general sufficient conditions for solutions of standard optimal control and variational problems. These conditions are sharper than the known ones. They are expressed in the form of inequalities which stem from the Hamilton-Jacobi method in terms of nonsmooth analysis. In the presence of smoothness the conditions are transformed so as to involve first and then second orders of differentiation. The results are applied to an example given by F. H. Clarke [”Optimization and nonsmooth analysis”, Wiley (1983)].
Reviewer: M.Armsen

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
49L99 Hamilton-Jacobi theories
49K05 Optimality conditions for free problems in one independent variable
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