Convex Processes and Hamiltonian Dynamical Systems

  • R. T. Rockafellar
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 168)


Many economists have studied optimal growth models of the form
$$\matrix{{\max imize} \hfill & {f_0^\infty e^{ - \rho } U(k(t),\,\,z(t))dt} \hfill \cr {subject\,\,to} \hfill & {k(0) = k_0, \dot k(t) = z(t) - \gamma k(t),} \hfill \cr }$$
where K is a vector of capital goods, γ is the rate of depreciation, ρ is the discount rate, and U is a continuous concave utility function defined on a closed convex set D in which the pair (k,z) is constrained to lie. The theory of such problems is plagued by technical difficulties caused by the infinite time interval.\The optimality conditions are still not well understood, and there are serious questions about the existence of solutions and even the meaningfulness, in certain cases, of the expression being maximized.


Saddle Point Hamiltonian System Constraint Qualification Infinite Time Interval Hamiltonian Dynamical System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • R. T. Rockafellar
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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