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Another view of the maximum principle for infinite-horizon optimal control problems in economics. (English. Russian original) Zbl 1480.49022

Russ. Math. Surv. 74, No. 6, 963-1011 (2019); translation from Usp. Mat. Nauk 74, No. 6, 3-54 (2019).
Summary: The authors present their recently developed complete version of the Pontryagin maximum principle for a class of infinite-horizon optimal control problems arising in economics. The main distinguishing feature of the result is that the adjoint variable is explicitly specified by a formula analogous to the Cauchy formula for solutions of linear differential systems. In certain situations this formula implies the ‘standard’ transversality conditions at infinity. Moreover, it can serve as an alternative to them. Examples demonstrate the advantages of the proposed version of the maximum principle. In particular, its applications are considered to Halkin’s example, to Ramsey’s optimal economic growth model, and to a basic model for optimal extraction of a non-renewable resource. Also presented is an economic interpretation of the characterization obtained for the adjoint variable.

MSC:

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