Abstract
A well-known sufficient condition for optimality is expressed in terms of a continuously differentiable function which is a solution to the Hamilton-Jacobi equation of Dynamic Programming. (A function which serves this purpose is called a Caratheodory function.) However a continuously differentiable may fail to exist, and this limits the usefulness of the condition as classically formulated. Here we ask, how might the condition be modified to extend its applicability? Emphasis is given to problems involving terminal constraints on the trajectories. These pose a special challenge since there is no obvious candidate for a Caratheodory function; we must surmise its existence from abstract arguments, or construct it as the value function of an auxiliary problem. Some interesting connections are made with the theory of necessary conditions.
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© 1985 Springer-Verlag
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Vinter, R.B. (1985). Dynamic programming for optimal control problems with terminal constraints. In: Dolcetta, I.C., Fleming, W.H., Zolezzi, T. (eds) Recent Mathematical Methods in Dynamic Programming. Lecture Notes in Mathematics, vol 1119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074786
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DOI: https://doi.org/10.1007/BFb0074786
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