On transversality condition for overtaking optimality in infinite horizon control problem

Dmitry Khlopin

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arXiv · 1704.03053

On transversality condition for overtaking optimality in infinite horizon control problem

Dmitry Khlopin

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Abstract

In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we construct a boundary condition on the co-state arc that is necessary for the optimality. We also show that, under additional assumptions on the payoff function's asymptotic behavior, the Pontryagin Maximum Principle with this condition becomes a complete system of relations, and this boundary condition points out the unique co-state arc through a Cauchy-type formula. An example is given to clarify the application of this formula as an explicit expression of the co-state arc. The cornerstone of this paper is the theorem on convergence of subdifferentials.

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Dmitry Khlopin. 2017-04-10. On transversality condition for overtaking optimality in infinite horizon control problem. https://arxiv.org/abs/1704.03053

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