Vol. 33, No. 2, 1970

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Generalized Hamiltonian equations for convex problems of Lagrange

Ralph Tyrrell Rockafellar

Vol. 33 (1970), No. 2, 411–427

Many nonclassical problems in the calculus of variations, arising for example from control theory, correspond in a sense to “Hamiltonian” functions which are not everywhere differentiable, but are convex in one vector argument and concave in the other. Optimal arcs in such problems satisfy generalized ordinary differential equations, defined in terms of subgradients of the “Hamiltonian.” Such equations are treated in this paper by convexity methods. An existence theorem is derived from a result of Castaing, and various properties of solutions are established.

Mathematical Subject Classification
Primary: 49.20
Received: 14 November 1969
Published: 1 May 1970
Ralph Tyrrell Rockafellar