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Hamiltonian trajectories and saddle points in mathematical economics

Rockafellar R. T.

Control and Cybernetics

2009

Vol. 38, no 4B

1575-1588

Infinite-horizon problems of kinds that arise in macroeconomic applications present a challenge in optimal control which has only partially been met. Results from the theory of convex problems of Lagrange can be utilized, to some extent, the most interesting feature being that in these problems the analysis revolves about a rest point of the Hamiltonian, which is at the same time a saddle point of the Hamiltonian in the minimax sense. The prospect is that in this situation the Hamiltonian dynamical system exhibits saddle point behavior in the differential equation sense as well. Some results are provided in this direction and coordinated with notions of asymptotic optimization, which mathematical economists have worked with.