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The B oxstep Method for Large-Scale Optimization

Author

Listed:
  • R. E. Marsten

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • W. W. Hogan

    (Federal Energy Administration, Washington, D. C.)

  • J. W. Blankenship

    (Institute for Defense Analyses, Arlington, Virginia)

Abstract

A new strategy is presented for large-scale optimization. The B oxstep method creates an algorithmic continuum between feasible-directions methods and cutting-plane methods. Several specific applications are described and computational results are reported.

Suggested Citation

  • R. E. Marsten & W. W. Hogan & J. W. Blankenship, 1975. "The B oxstep Method for Large-Scale Optimization," Operations Research, INFORMS, vol. 23(3), pages 389-405, June.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:3:p:389-405
    DOI: 10.1287/opre.23.3.389
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    Cited by:

    1. C. Arbib & F. Marinelli, 2009. "Exact and Asymptotically Exact Solutions for a Class of Assortment Problems," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 13-25, February.
    2. Veaceslav Ghilas & Jean-François Cordeau & Emrah Demir & Tom Van Woensel, 2018. "Branch-and-Price for the Pickup and Delivery Problem with Time Windows and Scheduled Lines," Transportation Science, INFORMS, vol. 52(5), pages 1191-1210, October.
    3. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    4. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    5. Pierre Hansen & Jack Brimberg & Dragan Urošević & Nenad Mladenović, 2007. "Primal-Dual Variable Neighborhood Search for the Simple Plant-Location Problem," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 552-564, November.
    6. Tiago Andrade & Nikita Belyak & Andrew Eberhard & Silvio Hamacher & Fabricio Oliveira, 2022. "The p-Lagrangian relaxation for separable nonconvex MIQCQP problems," Journal of Global Optimization, Springer, vol. 84(1), pages 43-76, September.
    7. Šárka Štádlerová & Sanjay Dominik Jena & Peter Schütz, 2023. "Using Lagrangian relaxation to locate hydrogen production facilities under uncertain demand: a case study from Norway," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    8. Semih Atakan & Kerem Bülbül & Nilay Noyan, 2017. "Minimizing value-at-risk in single-machine scheduling," Annals of Operations Research, Springer, vol. 248(1), pages 25-73, January.
    9. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    10. José M. Valério de Carvalho, 2005. "Using Extra Dual Cuts to Accelerate Column Generation," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 175-182, May.
    11. Göke, Leonard & Schmidt, Felix & Kendziorski, Mario, 2024. "Stabilized Benders decomposition for energy planning under climate uncertainty," European Journal of Operational Research, Elsevier, vol. 316(1), pages 183-199.
    12. A. Pessoa & R. Sadykov & E. Uchoa & F. Vanderbeck, 2018. "Automation and Combination of Linear-Programming Based Stabilization Techniques in Column Generation," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 339-360, May.
    13. Sebastian Ruther & Natashia Boland & Faramroze G. Engineer & Ian Evans, 2017. "Integrated Aircraft Routing, Crew Pairing, and Tail Assignment: Branch-and-Price with Many Pricing Problems," Transportation Science, INFORMS, vol. 51(1), pages 177-195, February.
    14. Timo Gschwind & Stefan Irnich, 2017. "Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 541-556, March.
    15. Yixin Zhao & Torbjörn Larsson & Elina Rönnberg & Panos M. Pardalos, 2018. "The fixed charge transportation problem: a strong formulation based on Lagrangian decomposition and column generation," Journal of Global Optimization, Springer, vol. 72(3), pages 517-538, November.
    16. Daniel Porumbel & François Clautiaux, 2017. "Constraint Aggregation in Column Generation Models for Resource-Constrained Covering Problems," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 170-184, February.
    17. Luciano Costa & Claudio Contardo & Guy Desaulniers & Julian Yarkony, 2022. "Stabilized Column Generation Via the Dynamic Separation of Aggregated Rows," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1141-1156, March.
    18. Sebastian Kraul & Markus Seizinger & Jens O. Brunner, 2023. "Machine Learning–Supported Prediction of Dual Variables for the Cutting Stock Problem with an Application in Stabilized Column Generation," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 692-709, May.
    19. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    20. Jia, Menglei & Chen, Feng, 2023. "Upward scalable vehicle routing problem of automobile inbound logistics with pickup flexibility," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).

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