IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v75y2012i2p149-163.html
   My bibliography  Save this article

Quantitative stability of mixed-integer two-stage quadratic stochastic programs

Author

Listed:
  • Zhiping Chen
  • Youpan Han

Abstract

For our introduced mixed-integer quadratic stochastic program with fixed recourse matrices, random recourse costs, technology matrix and right-hand sides, we study quantitative stability properties of its optimal value function and optimal solution set when the underlying probability distribution is perturbed with respect to an appropriate probability metric. To this end, we first establish various Lipschitz continuity results about the value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of linear constraints. The obtained results extend earlier results about quantitative stability properties of stochastic integer programming and stability results for mixed-integer parametric quadratic programs. Copyright Springer-Verlag 2012

Suggested Citation

  • Zhiping Chen & Youpan Han, 2012. "Quantitative stability of mixed-integer two-stage quadratic stochastic programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 149-163, April.
    • Handle: RePEc:spr:mathme:v:75:y:2012:i:2:p:149-163
    DOI: 10.1007/s00186-010-0326-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-010-0326-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-010-0326-1?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. Svetlozar T. Rachev & Werner Römisch, 2002. "Quantitative Stability in Stochastic Programming: The Method of Probability Metrics," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 792-818, November.
    2. B. Curtis Eaves, 1971. "On Quadratic Programming," Management Science, INFORMS, vol. 17(11), pages 698-711, July.
    Full references (including those not matched with items on IDEAS)

    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. Yongchao Liu & Huifu Xu & Jane J. Ye, 2011. "Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 670-694, November.
    2. Musshoff, Oliver & Hirschauer, Norbert, 2004. "Optimierung unter Unsicherheit mit Hilfe stochastischer Simulation und Genetischer Algorithmen – dargestellt anhand der Optimierung des Produktionsprogramms eines Brandenburger Marktfruchtbetriebes," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 53(07), pages 1-16.
    3. Soonhui Lee & Tito Homem-de-Mello & Anton Kleywegt, 2012. "Newsvendor-type models with decision-dependent uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 189-221, October.
    4. D. Kuhn, 2009. "Convergent Bounds for Stochastic Programs with Expected Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 597-618, June.
    5. Erasmus, Barend & van Jaarsveld, Albert & van Zyl, Johan & Vink, Nick, 2000. "The effects of climate change on the farm sector in the Western Cape," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 39(4), pages 1-15, December.
    6. Luo, Z-Q. & Zhang, S., 1997. "On the extensions of the Frank-Worfe theorem," Econometric Institute Research Papers EI 9748/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Alexander Engau, 2017. "Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 119-134, January.
    8. René Henrion & Christian Küchler & Werner Römisch, 2009. "Scenario reduction in stochastic programming with respect to discrepancy distances," Computational Optimization and Applications, Springer, vol. 43(1), pages 67-93, May.
    9. Louhichi, Kamel & Flichman, Guillermo & Blanco Fonseca, Maria, 2009. "A generic template for FSSIM," Reports 57463, Wageningen University, SEAMLESS: System for Environmental and Agricultural Modelling; Linking European Science and Society.
    10. Paudel, K. P. & Lohr, L. & Martin, N. R., 2000. "Effect of risk perspective on fertilizer choice by sharecroppers," Agricultural Systems, Elsevier, vol. 66(2), pages 115-128, November.
    11. Francesca Maggioni & Matteo Cagnolari & Luca Bertazzi, 2019. "The value of the right distribution in stochastic programming with application to a Newsvendor problem," Computational Management Science, Springer, vol. 16(4), pages 739-758, October.
    12. Just, Richard E., 2000. "Some Guiding Principles for Empirical Production Research in Agriculture," Agricultural and Resource Economics Review, Cambridge University Press, vol. 29(2), pages 138-158, October.
    13. Norton, George W., 1976. "Constraints To Increasing Livestock Production In Less Developed Countries: A Literature Review," Staff Papers 14043, University of Minnesota, Department of Applied Economics.
    14. Steffen Rebennack, 2022. "Data-driven stochastic optimization for distributional ambiguity with integrated confidence region," Journal of Global Optimization, Springer, vol. 84(2), pages 255-293, October.
    15. Vlasta Kaňková, 2013. "Risk Measures in Optimization Problems via Empirical Estimates," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 7(3), pages 162-177, November.
    16. Adams, Richard M. & Menkhaus, Dale J. & Woolery, Bruce A., 1980. "Alternative Parameter Specification In E, V Analysis: Implications For Farm Level Decision Making," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 5(01), pages 1-8, July.
    17. Yongchao Liu & Huifu Xu & Gui-Hua Lin, 2012. "Stability Analysis of One Stage Stochastic Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 537-555, February.
    18. Anderson, Jock R., 1975. "Programming For Efficient Planning Against Non-Normal Risk," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 19(2), pages 1-14, August.
    19. Hardaker, J. Brian & Pandey, Sushil & Patten, Louise H., 1991. "Farm Planning under Uncertainty: A Review of Alternative Programming Models," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 59(01), pages 1-14, April.
    20. Walker, Odell L. & Hardin, Mike L. & Mapp, Harry P., Jr. & Roush, Clint E., 1979. "Farm Growth And Estate Transfer In An Uncertain Environment," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 11(01), pages 1-12, July.

    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:mathme:v:75:y:2012:i:2:p:149-163. 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.