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Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces

Author

Listed:
  • Hélène Frankowska

    (Centre National de la Recherche Scientifique, Institut de Mathématiques de Jussieu–Paris Rive Gauche, Sorbonne Université, 75005 Paris, France)

  • Nobusumi Sagara

    (Department of Economics, Hosei University, Tokyo 194-0298, Japan)

Abstract

We investigate the value function of an infinite horizon variational problem in the infinite-dimensional setting. First, we provide an upper estimate of its Dini–Hadamard subdifferential in terms of the Clarke subdifferential of the Lipschitz continuous integrand and the Clarke normal cone to the graph of the set-valued mapping describing dynamics. Second, we derive a necessary condition for optimality in the form of an adjoint inclusion that grasps a connection between the Euler–Lagrange condition and the maximum principle. The main results are applied to the derivation of the necessary optimality condition of the spatial Ramsey growth model.

Suggested Citation

  • Hélène Frankowska & Nobusumi Sagara, 2022. "Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 320-340, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:320-340
    DOI: 10.1287/moor.2021.1130
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