The Pontryagin Maximum Principle for Infinite-Horizon Optimal Controls
Abstract
this paper (motivated by recent works on optimization of long-term economic growth) suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove new versions of the Pontryagin maximum principle. A special attention is paid to behavior of the adjoint variables and the Hamiltonian. Typical cases, in which standard transversality conditions hold at infinity, are described. Several significant earlier results are generalized.