IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v23y2015i4p877-898.html
   My bibliography  Save this article

A regularized simplex method

Author

Listed:
  • Csaba Fábián
  • Krisztián Eretnek
  • Olga Papp

Abstract

In case of a special problem class, the simplex method can be implemented as a cutting-plane method that approximates a polyhedral convex objective function. In this paper we consider a regularized version of this cutting-plane method, and interpret the resulting procedure as a regularized simplex method. (Regularization is performed in the dual space and only affects the process through the pricing mechanism. Hence the resulting method moves among basic solutions.) We present algorithmic details of this regularized simplex method, and favorable test results with our implementation. For general linear programming problems, we propose a Newton-type approach which requires the solution of a sequence of special problems. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Csaba Fábián & Krisztián Eretnek & Olga Papp, 2015. "A regularized simplex method," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 877-898, December.
  • Handle: RePEc:spr:cejnor:v:23:y:2015:i:4:p:877-898
    DOI: 10.1007/s10100-014-0344-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10100-014-0344-9
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10100-014-0344-9?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. Joseph Elble & Nikolaos Sahinidis, 2012. "Scaling linear optimization problems prior to application of the simplex method," Computational Optimization and Applications, Springer, vol. 52(2), pages 345-371, June.
    2. Claudia Sagastizábal & Mikhail Solodov, 2012. "Solving generation expansion planning problems with environmental constraints by a bundle method," Computational Management Science, Springer, vol. 9(2), pages 163-182, May.
    3. Csaba Fábián & Olga Papp & Krisztián Eretnek, 2013. "Implementing the simplex method as a cutting-plane method, with a view to regularization," Computational Optimization and Applications, Springer, vol. 56(2), pages 343-368, October.
    4. Csaba Fábián & Gautam Mitra & Diana Roman & Victor Zverovich, 2011. "An enhanced model for portfolio choice with SSD criteria: a constructive approach," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1525-1534.
    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. Botond Bertók & Tibor Csendes & Tibor Illés, 2015. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 811-813, December.

    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. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    2. Seyoung Park & Eun Ryung Lee & Sungchul Lee & Geonwoo Kim, 2019. "Dantzig Type Optimization Method with Applications to Portfolio Selection," Sustainability, MDPI, vol. 11(11), pages 1-32, June.
    3. Roman, Diana & Mitra, Gautam & Zverovich, Victor, 2013. "Enhanced indexation based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 228(1), pages 273-281.
    4. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs," Annals of Operations Research, Springer, vol. 318(1), pages 383-423, November.
    5. Francesco Cesarone & Justo Puerto, 2024. "New approximate stochastic dominance approaches for Enhanced Indexation models," Papers 2401.12669, arXiv.org.
    6. Zhidong Bai & Hua Li & Michael McAleer & Wing-Keung Wong, 2015. "Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 889-900, May.
    7. Sultan Almotairi & Elsayed Badr & Mustafa Abdul Salam & Hagar Ahmed, 2023. "Breast Cancer Diagnosis Using a Novel Parallel Support Vector Machine with Harris Hawks Optimization," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    8. Hashemi, Seyed Mohsen & Tabarzadi, Mahdi & Fallahi, Farhad & Rostam Niakan Kalhori, Masoumeh & Abdollahzadeh, Davood & Qadrdan, Meysam, 2024. "Water and emission constrained generation expansion planning for Iran power system," Energy, Elsevier, vol. 288(C).
    9. Renato Bruni & Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2012. "A new stochastic dominance approach to enhanced index tracking problems," Economics Bulletin, AccessEcon, vol. 32(4), pages 3460-3470.
    10. Renato Bruni & Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2013. "No arbitrage and a linear portfolio selection model," Economics Bulletin, AccessEcon, vol. 33(2), pages 1247-1258.
    11. Bruni, Renato & Cesarone, Francesco & Scozzari, Andrea & Tardella, Fabio, 2017. "On exact and approximate stochastic dominance strategies for portfolio selection," European Journal of Operational Research, Elsevier, vol. 259(1), pages 322-329.
    12. Renato Bruni & Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2012. "A New Lp Model For Enhanced Indexation," Departmental Working Papers of Economics - University 'Roma Tre' 0168, Department of Economics - University Roma Tre.
    13. Seddighi, Amir Hossein & Ahmadi-Javid, Amir, 2015. "Integrated multiperiod power generation and transmission expansion planning with sustainability aspects in a stochastic environment," Energy, Elsevier, vol. 86(C), pages 9-18.
    14. Neslihan Fidan Keçeci & Viktor Kuzmenko & Stan Uryasev, 2016. "Portfolios Dominating Indices: Optimization with Second-Order Stochastic Dominance Constraints vs. Minimum and Mean Variance Portfolios," JRFM, MDPI, vol. 9(4), pages 1-14, October.
    15. H Mezali & J E Beasley, 2013. "Quantile regression for index tracking and enhanced indexation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(11), pages 1676-1692, November.
    16. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.
    17. Jianming Xia, 2023. "Benchmark Beating with the Increasing Convex Order," Papers 2311.01692, arXiv.org.
    18. Nilay Noyan & Gábor Rudolf, 2013. "Optimization with Multivariate Conditional Value-at-Risk Constraints," Operations Research, INFORMS, vol. 61(4), pages 990-1013, August.
    19. Maciej Rysz & Alexander Vinel & Pavlo Krokhmal & Eduardo L. Pasiliao, 2015. "A Scenario Decomposition Algorithm for Stochastic Programming Problems with a Class of Downside Risk Measures," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 416-430, May.
    20. Maria Teresa Vespucci & Marida Bertocchi & Laureano F. Escudero & Stefano Zigrino, 2013. "A risk averse stochastic optimization model for power generation capacity expansion," Working Papers (2013-) 1305_qum, University of Bergamo, Department of Management, Economics and Quantitative Methods.

    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:cejnor:v:23:y:2015:i:4:p:877-898. 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.