IDEAS home Printed from https://ideas.repec.org/p/wop/iasawp/wp96020.html
   My bibliography  Save this paper

On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions

Author

Listed:
  • G.C. Pflug
  • A. Ruszczynski
  • R. Schultz

Abstract

Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions, it is proved that uniform convergence of empirical approximations of the right hand sides of the constraints implies uniform convergence of the optimal values in the linear and convex case.

Suggested Citation

  • G.C. Pflug & A. Ruszczynski & R. Schultz, 1996. "On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions," Working Papers wp96020, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp96020
    as

    Download full text from publisher

    File URL: http://www.iiasa.ac.at/Publications/Documents/WP-96-020.pdf
    Download Restriction: no
    File URL: http://www.iiasa.ac.at/Publications/Documents/WP-96-020.ps
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lucchetti, R. & Salinetti, G. & Wets, R. J. B., 1994. "Uniform Convergence of Probability Measures: Topological Criteria," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 252-264, November.
    2. Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, University Library of Munich, Germany, revised 13 Nov 2003.
    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. Georg Pflug & Andrzej Ruszczyński & Rüdiger Schultz, 1998. "On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 39-49, 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. E. Nasakkala & J. Keppo, 2008. "Hydropower with Financial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 503-529.
    2. Avilés A., Camilo & Oliva H., Sebastian & Watts, David, 2019. "Single-dwelling and community renewable microgrids: Optimal sizing and energy management for new business models," Applied Energy, Elsevier, vol. 254(C).
    3. Möst, Dominik & Keles, Dogan, 2010. "A survey of stochastic modelling approaches for liberalised electricity markets," European Journal of Operational Research, Elsevier, vol. 207(2), pages 543-556, December.
    4. Yong Zeng & Yanpeng Cai & Guohe Huang & Jing Dai, 2011. "A Review on Optimization Modeling of Energy Systems Planning and GHG Emission Mitigation under Uncertainty," Energies, MDPI, vol. 4(10), pages 1-33, October.
    5. Ventosa, Mariano & Baillo, Alvaro & Ramos, Andres & Rivier, Michel, 2005. "Electricity market modeling trends," Energy Policy, Elsevier, vol. 33(7), pages 897-913, May.
    6. Raimund M. Kovacevic, 2019. "Valuation and pricing of electricity delivery contracts: the producer’s view," Annals of Operations Research, Springer, vol. 275(2), pages 421-460, April.
    7. Finn R. Førsund, 2015. "Hydropower Economics," International Series in Operations Research and Management Science, Springer, edition 2, number 978-1-4899-7519-5, December.
    8. Marco Colombo & Andreas Grothey, 2013. "A decomposition-based crash-start for stochastic programming," Computational Optimization and Applications, Springer, vol. 55(2), pages 311-340, June.
    9. Bungener, Stephane & Hackl, Roman & Van Eetvelde, Greet & Harvey, Simon & Marechal, Francois, 2015. "Multi-period analysis of heat integration measures in industrial clusters," Energy, Elsevier, vol. 93(P1), pages 220-234.
    10. Fleten, Stein-Erik & Haugstvedt, Daniel & Steinsbø, Jens Arne & Belsnes, Michael & Fleischmann, Franziska, 2011. "Bidding hydropower generation: Integrating short- and long-term scheduling," MPRA Paper 44450, University Library of Munich, Germany.
    11. Klein Haneveld, Willem K. & Vlerk, Maarten H. van der, 2002. "Integrated chance constraints: reduced forms and an algorithm," Research Report 02A33, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    12. Hewings, Geoffrey J.D. & Dridi, Chokri & Guilhoto, Joaquim J.M., 2005. "Impacts of reallocation of resource constraints on the northeast economy of Brazil," MPRA Paper 38210, University Library of Munich, Germany.
    13. Michael Chen & Sanjay Mehrotra & Dávid Papp, 2015. "Scenario generation for stochastic optimization problems via the sparse grid method," Computational Optimization and Applications, Springer, vol. 62(3), pages 669-692, December.
    14. Fleten, Stein-Erik & Kristoffersen, Trine Krogh, 2007. "Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer," European Journal of Operational Research, Elsevier, vol. 181(2), pages 916-928, September.
    15. Conejo, Antonio J., 2001. "A decomposition procedure based on approximate newton directions," DES - Working Papers. Statistics and Econometrics. WS ws010906, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Gro Klaeboe & Anders Lund Eriksrud & Stein-Erik Fleten, 2013. "Benchmarking time series based forecasting models for electricity balancing market prices," Working Papers 2013-006, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    17. Lang, Joachim & Madlener, Reinhard, 2010. "Portfolio Optimization for Power Plants: The Impact of Credit Risk Mitigation and Margining," FCN Working Papers 11/2010, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    18. Wiedenmann, Susanne & Geldermann, Jutta, 2015. "Supply planning for processors of agricultural raw materials," European Journal of Operational Research, Elsevier, vol. 242(2), pages 606-619.
    19. Geman, Hélyette & Ohana, Steve, 2008. "Time-consistency in managing a commodity portfolio: A dynamic risk measure approach," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 1991-2005, October.
    20. Andrea Beltratti & Andrea Consiglio & Stavros Zenios, 1999. "Scenario modeling for the management ofinternational bond portfolios," Annals of Operations Research, Springer, vol. 85(0), pages 227-247, January.

    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:wop:iasawp:wp96020. 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: Thomas Krichel (email available below). General contact details of provider: https://edirc.repec.org/data/iiasaat.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.