IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v130y2006i1d10.1007_s10957-006-9089-5.html
   My bibliography  Save this article

Reciprocal Optimal Control Problems and the Associated Pareto Frontier

Author

Listed:
  • L. Grosset

    (University of Padova)

  • B. Viscolani

    (University of Padova)

Abstract

It is well known that, if a control is Pareto optimal for a multiobjective optimal control problem, then it satisfies the necessary conditions of an optimal control problem with isoperimetric constraints. We introduce a set of sufficient conditions reversing that implication. Thus, we study some properties of the isoperimetric problems and their applications to the analysis of economic models.

Suggested Citation

  • L. Grosset & B. Viscolani, 2006. "Reciprocal Optimal Control Problems and the Associated Pareto Frontier," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 113-123, July.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:1:d:10.1007_s10957-006-9089-5
    DOI: 10.1007/s10957-006-9089-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9089-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-006-9089-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Caputo,Michael R., 2005. "Foundations of Dynamic Economic Analysis," Cambridge Books, Cambridge University Press, number 9780521842723, January.
    2. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, November.
    3. M. R. Caputo, 1998. "Economic Characterization of Reciprocal Isoperimetric Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 325-350, August.
    4. M. R. Caputo, 1999. "Economic Characterization of Reciprocal Isoperimetric Control Problems Revisited," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 723-730, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Haijun Liu & Neng Fan & Panos M. Pardalos, 2012. "Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 370-381, August.
    2. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akpalu, Wisdom & Parks, Peter J., 2007. "Natural resource use conflict: gold mining in tropical rainforest in Ghana," Environment and Development Economics, Cambridge University Press, vol. 12(1), pages 55-72, February.
    2. Akpalu, Wisdom & Vondolia, Godwin K., 2012. "Bioeconomic model of spatial fishery management in developing countries," Environment and Development Economics, Cambridge University Press, vol. 17(2), pages 145-161, April.
    3. Savin Treanţă, 2022. "Lagrange-Hamilton Approach in Optimization Problems with Isoperimetric-Type Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 508-520, August.
    4. Becker, Daniel Thomas, 2008. "Dynamic tax competition and public-sector modernisation," Thuenen-Series of Applied Economic Theory 56, University of Rostock, Institute of Economics.
    5. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    6. Alice Issanchou & Karine Daniel & Pierre Dupraz & Carole Ropars-Collet, 2018. "Soil resource and the profitability and sustainability of farms: A soil quality investment model," Working Papers SMART 18-01, INRAE UMR SMART.
    7. Alvarez-Cuadrado, Francisco & Long, Ngo & Poschke, Markus, 2017. "Capital-labor substitution, structural change and growth," Theoretical Economics, Econometric Society, vol. 12(3), September.
    8. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    9. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    10. Crettez, Bertrand & Hayek, Naila & Zaccour, Georges, 2023. "When is frugality optimal?," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 65-75.
    11. Fritz, Oliver M. & Sonis, Michael & Hewings, Geoffrey J. D., 1998. "A Miyazawa analysis of interactions between polluting and non-polluting sectors," Structural Change and Economic Dynamics, Elsevier, vol. 9(3), pages 289-305, September.
    12. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    13. Chen Ling & Michael Caputo, 2012. "The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 313-334, September.
    14. Jan Zabojnik, 2011. "Subjective Evaluations With Performance Feedback," Working Paper 1283, Economics Department, Queen's University.
    15. Cheng, John Q & Wellman, Michael P, 1998. "The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes," Computational Economics, Springer;Society for Computational Economics, vol. 12(1), pages 1-24, August.
    16. Giorgio Giorgi, 2022. "Nonsingular M-matrices: a Tour in the Various Characterizations and in Some Related Classes," DEM Working Papers Series 206, University of Pavia, Department of Economics and Management.
    17. Georg Meran & Christian Hirschhausen, 2009. "A modified yardstick competition mechanism," Journal of Regulatory Economics, Springer, vol. 35(3), pages 223-245, June.
    18. Josa-Fombellida, Ricardo & Navas, Jorge, 2020. "Time consistent pension funding in a defined benefit pension plan with non-constant discounting," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 142-153.
    19. Thanh Tran & Kanghyun Yoon & Stefan Genchev, 2017. "Lump‐Sum versus Pay‐As‐You‐Go: The Moderating Effect of Contract Types on the Optimal Logistics Decisions," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 38(4), pages 547-555, June.
    20. Bolin, Kristian & Lindgren, Björn, 2014. "Non-monotonic health behaviours - implications for individual health-related behaviour in a demand-for-health framework," Working Papers in Economics 588, University of Gothenburg, Department of Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:130:y:2006:i:1:d:10.1007_s10957-006-9089-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.