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Envelope Theorems in Dynamic Programming

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Abstract

The envelope theorem is a statement about derivatives along an optimal trajectory. In dynamic programming the envelope theorem can be used to characterize and compute the optimal value function from its derivatives. We illustrate this here for the linear-quadratic control problem, the resource allocation problem, and the inverse problem of dynamic programming.

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Authors and Affiliations

  1. Jefferies & Co. Harborside Financial Center, Plaza III, Jersey City, NJ, 07311, USA

    Fuan Zhao

  2. RUTCOR – Rutgers Center for Operations Research, Rutgers University, 640 Bartholomew Rd, Piscataway, NJ, 08854-8003, USA

    Adi Ben-Israel

Authors
  1. Fuan Zhao
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  2. Adi Ben-Israel
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Zhao, F., Ben-Israel, A. Envelope Theorems in Dynamic Programming. Annals of Operations Research 101, 383–390 (2001). https://doi.org/10.1023/A:1010978103974

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  • DOI: https://doi.org/10.1023/A:1010978103974

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