IDEAS home Printed from https://ideas.repec.org/a/spr/decfin/v43y2020i2d10.1007_s10203-020-00288-6.html
   My bibliography  Save this article

Underestimation functions for a rank-two partitioning method

Author

Listed:
  • Riccardo Cambini

    (University of Pisa)

Abstract

Low-rank problems are nothing but nonlinear minimization problems over polyhedrons where a linear transformation of the variables provides an objective function which actually depends on very few variables. These problems are often used in applications, for example, in concave quadratic minimization problems, multiobjective/bicriteria programs, location–allocation models, quantitative management science, data envelopment analysis, efficiency analysis and performance measurement. The aim of this paper is to deepen on the study of a solution method for a class of rank-two nonconvex problems having a polyhedral feasible region expressed by means of inequality/box constraints and an objective function of the kind $$\phi (c^Tx+c_0,d^Tx+d_0)$$ ϕ ( c T x + c 0 , d T x + d 0 ) . The rank-two structure of the problem allows to determine various localization conditions and underestimation functions. The stated theoretical conditions allow to determine a solution algorithm for the considered class of rank-two problems whose performance is witnessed by means of a deep computational test.

Suggested Citation

  • Riccardo Cambini, 2020. "Underestimation functions for a rank-two partitioning method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 465-489, December.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:2:d:10.1007_s10203-020-00288-6
    DOI: 10.1007/s10203-020-00288-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10203-020-00288-6
    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/s10203-020-00288-6?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. Riccardo Cambini & Claudio Sodini, 2002. "A Finite Algorithm for a Particular D.C. Quadratic Programming Problem," Annals of Operations Research, Springer, vol. 117(1), pages 33-49, November.
    2. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    3. Riccardo Cambini & Claudio Sodini, 2008. "A sequential method for a class of box constrained quadratic programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 223-243, April.
    4. Riccardo Cambini & Claudio Sodini, 2010. "Global optimization of a rank-two nonconvex program," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 165-180, February.
    5. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
    6. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, September.
    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. Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.

    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. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
    2. Peiping Shen & Dianxiao Wu & Kaimin Wang, 2023. "Globally minimizing a class of linear multiplicative forms via simplicial branch-and-bound," Journal of Global Optimization, Springer, vol. 86(2), pages 303-321, June.
    3. Riccardo Cambini & Claudio Sodini, 2010. "Global optimization of a rank-two nonconvex program," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 165-180, February.
    4. Riccardo Cambini & Claudio Sodini, 2014. "A parametric solution algorithm for a class of rank-two nonconvex programs," Journal of Global Optimization, Springer, vol. 60(4), pages 649-662, December.
    5. Riccardo Cambini & Laura Carosi & Laura Martein & Ezat Valipour, 2017. "Simplex-like sequential methods for a class of generalized fractional programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 77-96, February.
    6. Khezrimotlagh, Dariush & Kaffash, Sepideh & Zhu, Joe, 2022. "U.S. airline mergers’ performance and productivity change," Journal of Air Transport Management, Elsevier, vol. 102(C).
    7. Christian Growitsch & Tooraj Jamasb & Christine Müller & Matthias Wissner, 2016. "Social Cost Efficient Service Quality: Integrating Customer Valuation in Incentive Regulation—Evidence from the Case of Norway," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, chapter 0, pages 71-91, Springer.
    8. Franz R. Hahn, 2007. "Determinants of Bank Efficiency in Europe. Assessing Bank Performance Across Markets," WIFO Studies, WIFO, number 31499, February.
    9. Alperovych, Yan & Hübner, Georges & Lobet, Fabrice, 2015. "How does governmental versus private venture capital backing affect a firm's efficiency? Evidence from Belgium," Journal of Business Venturing, Elsevier, vol. 30(4), pages 508-525.
    10. Wang, Zhao-Hua & Zeng, Hua-Lin & Wei, Yi-Ming & Zhang, Yi-Xiang, 2012. "Regional total factor energy efficiency: An empirical analysis of industrial sector in China," Applied Energy, Elsevier, vol. 97(C), pages 115-123.
    11. repec:lan:wpaper:1115 is not listed on IDEAS
    12. Ruiqing Yuan & Xiangyang Xu & Yanli Wang & Jiayi Lu & Ying Long, 2024. "Evaluating Carbon-Emission Efficiency in China’s Construction Industry: An SBM-Model Analysis of Interprovincial Building Heating," Sustainability, MDPI, vol. 16(6), pages 1-16, March.
    13. Azarnoosh Kafi & Behrouz Daneshian & Mohsen Rostamy-Malkhalifeh, 2021. "Forecasting the confidence interval of efficiency in fuzzy DEA," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 41-59.
    14. Costa, Marcelo Azevedo & Lopes, Ana Lúcia Miranda & de Pinho Matos, Giordano Bruno Braz, 2015. "Statistical evaluation of Data Envelopment Analysis versus COLS Cobb–Douglas benchmarking models for the 2011 Brazilian tariff revision," Socio-Economic Planning Sciences, Elsevier, vol. 49(C), pages 47-60.
    15. Kristiaan Kerstens & Ignace Van de Woestyne, 2018. "Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions," Annals of Operations Research, Springer, vol. 271(2), pages 1067-1078, December.
    16. Bo Li & Muhammad Mohiuddin & Qian Liu, 2019. "Determinants and Differences of Township Hospital Efficiency among Chinese Provinces," IJERPH, MDPI, vol. 16(9), pages 1-16, May.
    17. Ahmad, Usman, 2011. "Financial Reforms and Banking Efficiency: Case of Pakistan," MPRA Paper 34220, University Library of Munich, Germany.
    18. Nijkamp, P. & Stough, R. & Sahin, M., 2009. "Impact of social and human capital on business performance of migrant entrepreneurs - a comparative dutch-us study," Serie Research Memoranda 0017, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    19. Bowlin, W. F., 1995. "A characterization of the financial condition of the United States' aerospace-defense industrial base," Omega, Elsevier, vol. 23(5), pages 539-555, October.
    20. Mika Kortelainen & Timo Kuosmanen, 2007. "Eco-efficiency analysis of consumer durables using absolute shadow prices," Journal of Productivity Analysis, Springer, vol. 28(1), pages 57-69, October.
    21. Ashrafi, Ali & Seow, Hsin-Vonn & Lee, Lai Soon & Lee, Chew Ging, 2013. "The efficiency of the hotel industry in Singapore," Tourism Management, Elsevier, vol. 37(C), pages 31-34.

    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:decfin:v:43:y:2020:i:2:d:10.1007_s10203-020-00288-6. 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.