Geodesic
Relationship Between Dynamic Programming and the Maximum Principle Under State Constraints
Journal of convex analysis, Tome 6 (1999) no. 2, pp. 335-348.

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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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     author = {K.-E. Kim},
     title = {Relationship {Between} {Dynamic} {Programming} and the {Maximum} {Principle} {Under} {State} {Constraints}},
     journal = {Journal of convex analysis},
     pages = {335--348},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1999},
     url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a5/}
}
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K.-E. Kim. Relationship Between Dynamic Programming and the Maximum Principle Under State Constraints. Journal of convex analysis, Tome 6 (1999) no. 2, pp. 335-348. http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a5/