Envelope Theorems in Dynamic Programming

Fuan Zhao, Adi Ben-Israel

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Pages (from-to)383-390
Number of pages8
JournalAnnals of Operations Research
Issue number1-4
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


  • Dynamic programming
  • Envelope theorem
  • Inverse problem
  • Resource allocation

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