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The Dual Approach to Recursive Optimization: Theory and Examples

Author

Listed:
  • Nicola Pavoni

    (Bocconi University)

  • Christopher Sleet

    (Carnegie Mellon University)

  • Matthias Messner

    (Bocconi University)

Abstract

We bring together the theories of duality and dynamic programming. We show that the dual of a separable dynamic optimization problem can be recursively decomposed. We provide a dual version of the principle of optimality and give conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point. We relate primal and dual problems, address computational issues and give examples.

Suggested Citation

  • Nicola Pavoni & Christopher Sleet & Matthias Messner, 2014. "The Dual Approach to Recursive Optimization: Theory and Examples," 2014 Meeting Papers 1267, Society for Economic Dynamics.
    • Handle: RePEc:red:sed014:1267
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    References listed on IDEAS

    as
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    Cited by:

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    2. François Le Grand & Xavier Ragot, 2022. "Managing Inequality Over Business Cycles: Optimal Policies With Heterogeneous Agents And Aggregate Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 511-540, February.
    3. Yu, Meng & Zhang, Junnan, 2019. "Equilibrium in production chains with multiple upstream partners," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 1-10.
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    5. Meng Yu & Junnan Zhang, 2019. "Equilibrium in Production Chains with Multiple Upstream Partners," Papers 1908.08208, arXiv.org.
    6. Gaetano Bloise, 2020. "Unique Markov Equilibrium Under Limited Commitment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(2), pages 721-751, May.
    7. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    8. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    9. Can Urgun, 2021. "Restless Contracting," Working Papers 2021-88, Princeton University. Economics Department..
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    11. Jean Guillaume Forand & Jan Zapal, 2017. "The Demand and Supply of Favours in Dynamic Relationships," Working Papers 1705, University of Waterloo, Department of Economics, revised Sep 2017.
    12. Gaetano Bloise & Paolo Siconolfi, 2022. "A Negishi Approach to Recursive Contracts," Econometrica, Econometric Society, vol. 90(6), pages 2821-2855, November.
    13. Clayton, Christopher & Schaab, Andreas, 2022. "A Theory of Dynamic Inflation Targets," TSE Working Papers 22-1389, Toulouse School of Economics (TSE).
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    16. François Le Grand & Xavier Ragot, 2022. "Managing Inequality Over Business Cycles: Optimal Policies With Heterogeneous Agents And Aggregate Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 511-540, February.

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