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Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach

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  • Cuong Van

    ()

  • Raouf Boucekkine

    ()

  • Cagri Saglam

    ()

Abstract

In this paper, we make use of the Sobolev space W exp.1,1 (R+, R exp.n) 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 L exp.1 spaces have natural positive cones with no interior points.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 497-509, September.
  • Handle: RePEc:spr:joecth:v:32:y:2007:i:3:p:497-509
    DOI: 10.1007/s00199-006-0118-2
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    References listed on IDEAS

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    1. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March.
    2. Bonnisseau, Jean-Marc & Le Van, Cuong, 1996. "On the subdifferential of the value function in economic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 55-73.
    3. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
    4. Dana, R.A. & Le Van, C. & Magnien, F., 1994. "General Equilibrium in Asset Markets with or without Short-Selling," Papers 9492, Tilburg - Center for Economic Research.
    5. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
    6. Araujo,A. & Monteiro,P.K., 1989. "General equilibrium with infinitely many goods: The case of seperable utilities," Discussion Paper Serie A 249, University of Bonn, Germany.
    7. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
    8. Cuong Le Van, 1996. "Complete characterization of Yannelis-Zame and Chichilnisky-Kalman-Mas-Colell properness conditions on preferences for separable concave functions defined in $L^{p}_{+}.$ and Lp (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 155-166.
    9. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
    10. Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
    11. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
    12. Ngo Van Long & Koji Shimomura, 2003. "A Note on Transversality Conditions," Discussion Paper Series 144, Research Institute for Economics & Business Administration, Kobe University.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2014. "Infectious diseases and economic growth," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 34-53.
    5. Patrice Pieretti & Skerdilajda Zanaj & Benteng Zou, 2012. "On the long run economic performance of small economies," CREA Discussion Paper Series 12-14, Center for Research in Economic Analysis, University of Luxembourg.

    More about this item

    Keywords

    Optimal control; Sobolev spaces; Transversality conditions; Order ideal; C 61;

    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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