IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v91y2020i2d10.1007_s00186-019-00673-x.html
   My bibliography  Save this article

The blockwise coordinate descent method for integer programs

Author

Listed:
  • Sven Jäger

    (Technische Universität Berlin)

  • Anita Schöbel

    (TU Kaiserslautern
    Fraunhofer Institut für Techno- und Wirtschaftsmathematik ITWM)

Abstract

Blockwise coordinate descent methods have a long tradition in continuous optimization and are also frequently used in discrete optimization under various names. New interest in blockwise coordinate descent methods arises for improving sequential solutions for problems which consist of several planning stages. In this paper we systematically formulate and analyze the blockwise coordinate descent method for integer programming problems. We discuss convergence of the method and properties of the resulting solutions. We extend the notion of Pareto optimality for blockwise coordinate descent to the case that the blocks do not form a partition and compare Pareto optimal solutions to blockwise optimal and to global optimal solutions. Among others we derive a condition which ensures that the solution obtained by blockwise coordinate descent is weakly Pareto optimal and we confirm convergence of the blockwise coordinate descent to a global optimum in matroid polytopes. The results are interpreted in the context of multi-stage linear integer programming problems and illustrated for integrated planning in public transportation.

Suggested Citation

  • Sven Jäger & Anita Schöbel, 2020. "The blockwise coordinate descent method for integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 357-381, April.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:2:d:10.1007_s00186-019-00673-x
    DOI: 10.1007/s00186-019-00673-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-019-00673-x
    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/s00186-019-00673-x?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. Hawkins, Douglas M., 1994. "The feasible solution algorithm for least trimmed squares regression," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 185-196, February.
    2. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    3. Zvi Drezner & Said Salhi, 2017. "Incorporating neighborhood reduction for the solution of the planar p-median problem," Annals of Operations Research, Springer, vol. 258(2), pages 639-654, November.
    4. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    5. Ingmar Steinzen & Vitali Gintner & Leena Suhl & Natalia Kliewer, 2010. "A Time-Space Network Approach for the Integrated Vehicle- and Crew-Scheduling Problem with Multiple Depots," Transportation Science, INFORMS, vol. 44(3), pages 367-382, August.
    6. Hanne L. Petersen & Allan Larsen & Oli B. G. Madsen & Bjørn Petersen & Stefan Ropke, 2013. "The Simultaneous Vehicle Scheduling and Passenger Service Problem," Transportation Science, INFORMS, vol. 47(4), pages 603-616, November.
    7. Clifford Hildreth, 1957. "A quadratic programming procedure," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 4(1), pages 79-85, March.
    8. Guihaire, Valérie & Hao, Jin-Kao, 2008. "Transit network design and scheduling: A global review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(10), pages 1251-1273, December.
    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. Pan Shang & Yu Yao & Liya Yang & Lingyun Meng & Pengli Mo, 2021. "Integrated Model for Timetabling and Circulation Planning on an Urban Rail Transit Line: a Coupled Network-Based Flow Formulation," Networks and Spatial Economics, Springer, vol. 21(2), pages 331-364, June.
    2. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    3. Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
    4. Laporte, Gilbert & Ortega, Francisco A. & Pozo, Miguel A. & Puerto, Justo, 2017. "Multi-objective integration of timetables, vehicle schedules and user routings in a transit network," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 94-112.
    5. Daraio, Cinzia & Diana, Marco & Di Costa, Flavia & Leporelli, Claudio & Matteucci, Giorgio & Nastasi, Alberto, 2016. "Efficiency and effectiveness in the urban public transport sector: A critical review with directions for future research," European Journal of Operational Research, Elsevier, vol. 248(1), pages 1-20.
    6. Cinzia Daraio & Marco Diana & Flavia Di Costa & Claudio Leporelli & Giorgio Matteucci & Alberto Nastasi, 2014. "Efficiency and effectiveness in the urban public transport sector: a critical review with directions for future research," DIAG Technical Reports 2014-14, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    7. Kuo, Yong-Hong & Leung, Janny M.Y. & Yan, Yimo, 2023. "Public transport for smart cities: Recent innovations and future challenges," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1001-1026.
    8. Sarah Perrin & Thierry Roncalli, 2019. "Machine Learning Optimization Algorithms & Portfolio Allocation," Papers 1909.10233, arXiv.org.
    9. Fonseca, João Paiva & van der Hurk, Evelien & Roberti, Roberto & Larsen, Allan, 2018. "A matheuristic for transfer synchronization through integrated timetabling and vehicle scheduling," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 128-149.
    10. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    11. van Wee, Bert & Bohte, Wendy & Molin, Eric & Arentze, Theo & Liao, Feixiong, 2014. "Policies for synchronization in the transport–land-use system," Transport Policy, Elsevier, vol. 31(C), pages 1-9.
    12. Abheek Ghosh & Paul W. Goldberg, 2023. "Best-Response Dynamics in Lottery Contests," Papers 2305.10881, arXiv.org.
    13. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    14. Renaud Bourlès & Yann Bramoullé & Eduardo Perez‐Richet, 2017. "Altruism in Networks," Econometrica, Econometric Society, vol. 85, pages 675-689, March.
    15. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
    16. Wu, Weitiao & Lin, Yue & Liu, Ronghui & Jin, Wenzhou, 2022. "The multi-depot electric vehicle scheduling problem with power grid characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 322-347.
    17. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    18. Jung, Yoon Mo & Whang, Joyce Jiyoung & Yun, Sangwoon, 2020. "Sparse probabilistic K-means," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    19. Cao, Zhejing & Zhang, Xiaohu & Chua, Kelman & Yu, Honghai & Zhao, Jinhua, 2021. "E-scooter sharing to serve short-distance transit trips: A Singapore case," Transportation Research Part A: Policy and Practice, Elsevier, vol. 147(C), pages 177-196.
    20. Pawel Kalczynski & Jack Brimberg & Zvi Drezner, 2022. "Less is more: discrete starting solutions in the planar p-median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 34-59, April.
    21. Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.

    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:91:y:2020:i:2:d:10.1007_s00186-019-00673-x. 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.