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Journal of Convex Analysis 06 (1999), No. 2, 335--348
Copyright Heldermann Verlag 1999

Relationship Between Dynamic Programming and the Maximum Principle Under State Constraints

Kyung-Eung Kim
Dept. of Mathematics, Yonsei University, Seodaemoon-ku Shinchon-dong 134, Seoul, Southkorea

Bellman's dynamic programming and Pontryagin's maximum principle are two basic tools for studying optimal control theory. We consider the optimal control problem under state constraints and examine the relationship between the maximum principle and dynamic programming via the adjoint, Hamiltonian and value functions. For this purpose the notions of generalized superdifferentials are introduced.

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