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Value Functions and Transversality Conditions for Infinite-Horizon Optimal Control Problems

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An Erratum to this article was published on 17 March 2010

Abstract

This paper investigates a relationship between the maximum principle with an infinite horizon and dynamic programming and sheds new light upon the role of the transversality condition at infinity as necessary and sufficient conditions for optimality with or without convexity assumptions. We first derive the nonsmooth maximum principle and the adjoint inclusion for the value function as necessary conditions for optimality. We then present sufficiency theorems that are consistent with the strengthened maximum principle, employing the adjoint inequalities for the Hamiltonian and the value function. Synthesizing these results, necessary and sufficient conditions for optimality are provided for the convex case. In particular, the role of the transversality conditions at infinity is clarified.

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Authors and Affiliations

  1. Faculty of Economics, Hosei University, 4342, Aihara, Machida, Tokyo, 194–0298, Japan

    Nobusumi Sagara

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  1. Nobusumi Sagara
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Correspondence to Nobusumi Sagara.

Additional information

This research is supported by a Grant-in-Aid for Scientific Research (No. 18610003) from the Ministry of Education, Culture, Sports, Science and Technology. I am grateful to an anonymous referee and the editor of this journal for helpful comments.

An erratum to this article can be found at http://dx.doi.org/10.1007/s11228-010-0135-y

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Sagara, N. Value Functions and Transversality Conditions for Infinite-Horizon Optimal Control Problems. Set-Valued Anal 18, 1–28 (2010). https://doi.org/10.1007/s11228-009-0132-1

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