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Optimal control in infinite horizon problems: a Sobolev space approach

Author

Listed:
  • Cuong Le Van

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain)

  • Raouf Boucekkine

    (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain)

  • Cagri Saglam

    (Bilkent University [Ankara])

Abstract

In this paper, we make use of the Sobolev space W1,1(R+, Rn) to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L1 spaces have natural positive cones with no interior points.

Suggested Citation

  • Cuong Le Van & Raouf Boucekkine & Cagri Saglam, 2005. "Optimal control in infinite horizon problems: a Sobolev space approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00197546, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00197546
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00197546v1
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    2. Skerdilajda Zanaj & Patrice Pieretti & Benteng Zou, 2021. "On the long run sustainability of small jurisdictions," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 48(1), pages 15-35, March.
    3. Dogan, Erol & Le Van, Cuong & Saglam, Cagri, 2011. "Optimal timing of regime switching in optimal growth models: A Sobolev space approach," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 97-103, March.
    4. Greiner, Alfred & Bondarev, Anton, 2017. "Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds," Working papers 2017/06, Faculty of Business and Economics - University of Basel.
    5. Mahdi Ebrahimi Kahou & Jesse Perla & Geoff Pleiss, 2024. "Solving Models of Economic Dynamics with Ridgeless Kernel Regressions," Papers 2406.01898, arXiv.org, revised Oct 2025.
    6. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    7. Yoichi Otsubo & Theoharry Grammatikos & Thorsten Lehnert, 2012. "Market Perceptions of US and European Policy Actions Around the Subprime Crisis," DEM Discussion Paper Series 12-14, Department of Economics at the University of Luxembourg.
    8. Jean-Michel Grandmont, 2013. "Tribute to Cuong Le Van," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 5-10, March.
    9. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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