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Convexity and Duality in Hamilton-Jacobi Theory

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  • R.T. Rockafellar
  • P.R. Wolenski

Abstract

Value functions propagated from initial or terminal costs and constraints by way of a differential or more broadly through a Lagrangian that may take on "alpha," are studied in the case where convexity persists in the state argument. Such value functions, themselves taking on "alpha," are shown to satisfy a subgradient form of the Hamilton-Jacobi equation which strongly supports properties of local Lipschitz continuity, semidifferentibility and Clarke regularity. An extended `method of characteristics' is developed which determines them from Hamiltonian dynamics underlying the given Lagrangian. Close relations with a dual value function are revealed.

Suggested Citation

  • R.T. Rockafellar & P.R. Wolenski, 1998. "Convexity and Duality in Hamilton-Jacobi Theory," Working Papers ir98057, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:ir98057
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    1. Sánchez-Díaz, Iván & Holguín-Veras, José & Ban, Xuegang (Jeff), 2015. "A time-dependent freight tour synthesis model," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 144-168.

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