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Optimal control in infinite horizon problems: A Sobolev space approach

Author

Listed:
  • LE VAN, CUONG
  • BOUCEKKINE, Raouf
  • SAGLAM, Cagri

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.
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Suggested Citation

  • LE VAN, CUONG & BOUCEKKINE, Raouf & SAGLAM, Cagri, 2007. "Optimal control in infinite horizon problems: A Sobolev space approach," LIDAM Reprints CORE 1956, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1956
    DOI: 10.1007/s00199-006-0118-2
    Note: In : Economic Theory, 32, 497-509, 2007
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    7. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    8. Patrice Pieretti & Skerdilajda Zanaj & Benteng Zou, 2012. "On the long run economic performance of small economies," DEM Discussion Paper Series 12-14, Department of Economics at the University of Luxembourg.

    More about this item

    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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