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The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons. (English) Zbl 1072.49015

Summary: This paper 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. Special attention is paid to the 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.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
91B62 Economic growth models
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