Convex Analysis and Mathematical Economics pp 122-136 | Cite as

# Convex Processes and Hamiltonian Dynamical Systems

Conference paper

## Abstract

Many economists have studied optimal growth models of the form
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.

$$\matrix{{\max imize} \hfill & {f_0^\infty e^{ - \rho } U(k(t),\,\,z(t))dt} \hfill \cr {subject\,\,to} \hfill & {k(0) = k_0, \dot k(t) = z(t) - \gamma k(t),} \hfill \cr }$$

(1)

## Keywords

Saddle Point Hamiltonian System Constraint Qualification Infinite Time Interval Hamiltonian Dynamical System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1979