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Value Functions and Transversality Conditions for Infinite Horizon Optimal Control Problems

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Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2008)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 14))

Abstract

This paper investigates infinite horizon optimal control problems with fixed left endpoints with nonconvex, nonsmooth data. We derive the nonsmooth maximum principle and the adjoint inclusion for the value function as necessary conditions for optimality that indicate the relationship between the maximum principle and dynamic programming. The necessary conditions under consideration are extensions of those of [8] to an infinite horizon setting. We then present new sufficiency conditions consistent with the necessary conditions, which are motivated by the useful result by [26] whose sufficiency theorem is valid for nonconvex, nondifferentiable Hamiltonians. The sufficiency theorem presented in this paper employs the strengthened adjoint inclusion of the value function as well as the strengthened maximum principle. If we restrict our result to convex models, it is possible to characterize minimizing processes and provide necessary and sufficient conditions for optimality. 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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Editors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, UFR MIM,, Paul Verlaine University of Metz, Metz, France

    Hoai An Le Thi

  2. Faculty of Sciences, Technology and Communications, University of Luxembourg, Luxembourg

    Pascal Bouvry

  3. Laboratory of Mathematics, National Institute for Applied Sciences, Rouen Mont, Saint Aignan, France

    Tao Pham Dinh

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Sagara, N. (2008). Value Functions and Transversality Conditions for Infinite Horizon Optimal Control Problems. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO 2008. Communications in Computer and Information Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87477-5_30

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  • DOI: https://doi.org/10.1007/978-3-540-87477-5_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87476-8

  • Online ISBN: 978-3-540-87477-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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