IDEAS home Printed from https://ideas.repec.org/p/cor/louvrp/2241.html
   My bibliography  Save this paper

Solving infinite-dimensional optimizaiton problems by polynomial approximation

Author

Listed:
  • DEVOLDER, Olivier
  • GLINEUR, François
  • NESTEROV, Yurii

Abstract

In this paper, we solve a class of convex infinite-dimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we restrict the decision variable to a sequence of finite-dimensional linear subspaces of the original infinite-dimensional space and solve the corresponding finite-dimensional problems in a efficient way using structured convex optimization techniques. We prove that, under some reasonable assumptions, the sequence of these optimal values converges to the optimal value of the original infinite-dimensional problem and give an explicit description of the corresponding rate of convergence.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2010. "Solving infinite-dimensional optimizaiton problems by polynomial approximation," LIDAM Reprints CORE 2241, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2241
    Note: In : M. Diehl, F. Glineur, E. Jarlebring and W. Michiels (eds.), Recent Advances in Optimization and its Applications in ENgineering, Heidelberg, Springer, 37-46, 2010
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. NESTEROV, Yu., 2000. "Squared functional systems and optimization problems," LIDAM Reprints CORE 1472, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Pierre-Philippe Combes & Thierry Mayer & Jacques-François Thisse, 2008. "Economic Geography: The Integration of Regions and Nations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00311000, HAL.
    3. Huriot,Jean-Marie & Thisse,Jacques-François (ed.), 2009. "Economics of Cities," Cambridge Books, Cambridge University Press, number 9780521118279, October.
    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. Jubril, A.M. & Olaniyan, O.A. & Komolafe, O.A. & Ogunbona, P.O., 2014. "Economic-emission dispatch problem: A semi-definite programming approach," Applied Energy, Elsevier, vol. 134(C), pages 446-455.
    2. Kristina Rognlien Dahl, 2019. "A convex duality approach for pricing contingent claims under partial information and short selling constraints," Papers 1902.10492, arXiv.org.
    3. Kristina Rognlien Dahl, 2019. "Management of a hydropower system via convex duality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 43-71, February.

    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. Pierre Pestieau & Gregory Ponthière, 2012. "Long-Term Care Insurance Puzzle," Palgrave Macmillan Books, in: Joan Costa-Font & Christophe Courbage (ed.), Financing Long-Term Care in Europe, chapter 3, pages 41-52, Palgrave Macmillan.
    2. Gautier, Axel & Wauthy, Xavier, 2012. "Competitively neutral universal service obligations," Information Economics and Policy, Elsevier, vol. 24(3), pages 254-261.
    3. Bouezmarni, Taoufik & Van Bellegem, Sébastien, 2009. "Nonparametric Beta Kernel Estimator for Long Memory Time Series," IDEI Working Papers 633, Institut d'Économie Industrielle (IDEI), Toulouse.
    4. Pierre Pestieau & Maria Racionero, 2015. "Tagging with leisure needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 687-706, December.
    5. Luc Bauwens & Gary Koop & Dimitris Korobilis & Jeroen V.K. Rombouts, 2015. "The Contribution of Structural Break Models to Forecasting Macroeconomic Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 596-620, June.
    6. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Gautier Axel & Paolini Dimitri, 2011. "Universal Service Financing in Competitive Postal Markets: One Size Does Not Fit All," Review of Network Economics, De Gruyter, vol. 10(3), pages 1-30, September.
    8. Bréchet, Thierry & Jouvet, Pierre-André & Rotillon, Gilles, 2013. "Tradable pollution permits in dynamic general equilibrium: Can optimality and acceptability be reconciled?," Ecological Economics, Elsevier, vol. 91(C), pages 89-97.
    9. Cremer, Helmuth & Gahvari, Firouz & Pestieau, Pierre, 2011. "Fertility, human capital accumulation, and the pension system," Journal of Public Economics, Elsevier, vol. 95(11), pages 1272-1279.
    10. Leroux, Marie-Louise & Ponthiere, Gregory, 2013. "Utilitarianism and unequal longevities: A remedy?," Economic Modelling, Elsevier, vol. 30(C), pages 888-899.
    11. A. Mauleon & Vincent Vannetelbosch & Cecilia Vergari, 2014. "Unions' Relative Concerns And Strikes In Wage Bargaining," Bulletin of Economic Research, Wiley Blackwell, vol. 66(4), pages 374-383, October.
    12. M.-L. Leroux & P. Pestieau, 2012. "The political economy of derived pension rights," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 19(5), pages 753-776, October.
    13. Per J. Agrell & Axel Gautier, 2017. "A Theory of Soft Capture," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(3), pages 571-596, July.
    14. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
    15. RAMAEKERS, Eve, 2010. "Fair allocation of indivisible goods among two agents," LIDAM Discussion Papers CORE 2010087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Manzi, Jorge & San Martin, Ernesto & Van Bellegem, Sébastien, 2010. "School System Evaluation By Value-Added Analysis under Endogeneity," IDEI Working Papers 631, Institut d'Économie Industrielle (IDEI), Toulouse.
    17. Lefouili, Yassine & Roux, Catherine, 2012. "Leniency programs for multimarket firms: The effect of Amnesty Plus on cartel formation," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 624-640.
    18. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    19. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2013. "Multivariate Volatility Modeling Of Electricity Futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 743-761, August.
    20. GILLIS, Nicolas & GLINEUR, François, 2011. "Accelerated multiplicative updates and hierarchical als algorithms for nonnegative matrix factorization," LIDAM Discussion Papers CORE 2011030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Statistics

    Access and download statistics

    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:cor:louvrp:2241. 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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    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.